From banach-bounces at math.okstate.edu Fri Jan 4 12:00:27 2008 Return-Path: <banach-bounces at math.okstate.edu> From: Dale Alspach <alspach at math.okstate.edu> Subject: [Banach] Conference on Convex Geometry Reply-To: koldobsk at math.missouri.edu
Dear Colleagues, We would like to invite you to participate in the Conference on Convex Geometry in Columbia, Missouri in March 2008. There will be two mini-conferences - Classical Convex Geometry on March 21-23 and Asymptotic Convex Geometry on March 28-30. Please see the conference homepage at http://www.math.missouri.edu/calendar/FRG-08 which contains the list of speakers, accomodations and directions to Columbia, Missouri. Please take a minute to register at the website above. Best regards, Alex Koldobsky and Mark Rudelson _______________________________________________ Banach mailing list Banach at math.okstate.edu http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Wed Jan 16 10:38:31 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 545EFD0A4B; Wed, 16 Jan 2008 10:38:31 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Emanuel Milman Message-Id: <20080116163831.545EFD0A4B at fourier.math.okstate.edu> Date: Wed, 16 Jan 2008 10:38:31 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On the role of convexity in isoperimetry, spectral-gap and concentration" by Emanuel Milman. Abstract: We show that for convex domains in Euclidean space, Cheeger's isoperimetric inequality, Spectral-Gap of the Neumann Laplacian, Exponential concentration of 1-Lipschitz functions, and the a-priori weakest linear tail-decay of 1-Lipschitz functions, are all equivalent (to within universal constants). This substantially extends previous results of Maz'ya, Cheeger, Gromov--Milman, Buser and Ledoux. As an application, we conclude the stability of the Spectral-Gap for convex domains under convex perturbations which preserve volume (up to constants) and under maps which are ``on-average'' Lipschitz. We also easily recover (and extend) many previously known lower bounds, due to Payne--Weinberger, Li--Yau, Kannan--Lov\'asz--Simonovits, Bobkov and Sodin, on the Cheeger constant for convex domains. We also provide a new characterization of the Cheeger constant, as one over the expectation of the distance from the ``worst'' Borel set having half the measure of the convex domain. As a by-product of our methods, we develop a coherent single framework for passing between isoperimetric inequalities, Orlicz-Sobolev functional inequalities and q-capacities, the latter being notions introduced by Maz'ya and extended by Barthe--Cattiaux--Roberto. As an application, we extend the known results due to the latter authors about the stability of the isoperimetric profile under tensorization, when there is no Central-Limit obstruction. A crucial ingredient to our proof is a result from Riemannian Geometry on the concavity of the isoperimetric profile. Our results extend to the more general setting of Riemannian manifolds with density which satisfy the $CD(0,\infty)$ curvature-dimension condition of Bakry-\'Emery. Archive classification: math.MG math.FA Remarks: 70 pages, 1st version The source file(s), Dingir120.eps: 7755 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.4092 or http://arXiv.org/abs/0712.4092 or by email in unzipped form by transmitting an empty message with subject line uget 0712.4092 or in gzipped form by using subject line get 0712.4092 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Jan 18 08:24:42 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5B414D09C3; Fri, 18 Jan 2008 08:24:42 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan Message-Id: <20080118142442.5B414D09C3 at fourier.math.okstate.edu> Date: Fri, 18 Jan 2008 08:24:42 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Bregman distances and Chebyshev sets" by Heinz H. Bauschke, Xianfu Wang, Jane Ye, and Xiaoming Yuan. Abstract: A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given. Archive classification: math.FA Mathematics Subject Classification: Primary 41A65; Secondary 47H05, 49J52. The source file(s), submitted.tex: 67922 bytes, is(are) stored in gzipped form as 0712.4030.gz with size 19kb. The corresponding postcript file has gzipped size 134kb. Submitted from: heinz.bauschke at ubc.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0712.4030 or http://arXiv.org/abs/0712.4030 or by email in unzipped form by transmitting an empty message with subject line uget 0712.4030 or in gzipped form by using subject line get 0712.4030 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Thu Jan 17 21:59:11 2008 Return-Path: <banach-bounces at math.okstate.edu> From: "George A Anastassiou (ganastss)" <ganastss at memphis.edu> To: anna <anna at eureka.vu.edu.au>, atnet <at-net-dl at uni-giessen.de>, banach <banach at math.okstate.edu>, Dynamics <hsg at phy.duke.edu>, dynsys <dynsys at listserv.unc.edu>, "George A Anastassiou (ganastss)" <ganastss at memphis.edu>, nanet <na.digest at na-net.ornl.gov>, rgmia <rgmia at lists.vu.edu.au>, rgmia-request <rgmia-request at lists.vu.edu.au>, siam <helfrich at siam.org>, stochastic <bulletin at queue.Korea.ac.kr> Date: Thu, 17 Jan 2008 12:40:52 -0600 Thread-Topic: AMAT08 Thread-Index: AchZOHzIncKDYRr1ScSBez4jXBUo9A== Message-ID: <06CF1FBD4645F745B5A89221FF341DC324A6AE7D at itexbe7.uom.memphis.edu> Subject: [Banach] AMAT08
DEAR COLLEAQUES HI! CONFERENCE ANNOUNCEMENT: "International Conference on Applied Mathematics and Approximation Theory 2008", October 11-13,2008, University of Memphis, Memphis, TN, USA. Honoring 80th Birthday of P.L.Butzer (AMAT08). Plenary Speakers:C.Bardaro, J.Bona, B.Berndt, F.Deutsch, K.Diethelm, S.Dragomir, J.Goldstein, M.Ismail, M.J.Lai, H.Mhaskar, J.Prestin, S.Samko, R.Stens, A.Zayed. Organizer:George Anastassiou, http://www.msci.memphis.edu/AMAT2008/ PLEASE REGISTER-COME THANKS SINCERELY YOURS George A. Anastassiou,Ph.D DOCTOR HONORIS CAUSA Professor of Mathematics Department of Mathematical Sciences The University of Memphis,Memphis,TN 38152,USA Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series: Concrete & Applicable Math. Springer Consultant-Editor in computational math books Birkhauser Consultant Editor in A.M.Sci. CRC-A.M. Advisor NOVA MATH books ADVISOR ganastss at memphis.edu<mailto:ganastss at memphis.edu> http://www.eudoxuspress.com http://www.msci.memphis.edu/~ganastss/jocaaa http://www.msci.memphis.edu/~ganastss/jcaam http://www.msci.memphis.edu/~ganastss/jafa tel:(INT 001)- 901-678-3144 office 901-751-3553 home 901-678-2482 secr. Fax: 901-678-2480 Associate Editor in: J.Communications in Applied Analysis, Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO, J.Advances in non-linear Variational Inequalities, e-J.of Inequalities in Pure and Applied Math., Anals U.Oradea-Fasciola Mathematica, Journal of Inequalities and Applications, Inter.J.of Pure&Appl.Math.,MIA, Inter.J.of Computational and Numerical Analysis with Appl. President of World Soc.for study & promotion of Ancient Greek Mathematics Honorary Editor Australian Journal of Mathematical Analysis and Appl. Panamerican Mathematical Journal Eudoxus Press,LLC Pres.,ETC. _______________________________________________ Banach mailing list Banach at math.okstate.edu http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Sun Jan 20 07:54:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 98662D0999; Sun, 20 Jan 2008 07:54:46 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Gestur Olafsson and Boris Rubin Message-Id: <20080120135446.98662D0999 at fourier.math.okstate.edu> Date: Sun, 20 Jan 2008 07:54:46 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Invariant functions on Grassmannians" by Gestur Olafsson and Boris Rubin. Abstract: It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces dimension of its actual argument, hold for every compact symmetric space and can be obtained in the framework of Lie-theoretic consideration. In the present article, this phenomenon is given precise meaning for functions on the Grassmann manifold $G_{n,i}$ of $i$-dimensional subspaces of $\bbr^n$, which are invariant under orthogonal transformations preserving complementary coordinate subspaces of arbitrary fixed dimension. The corresponding integral formulas are obtained. Our method relies on bi-Stiefel decomposition and does not invoke Lie theory. Archive classification: math.FA Mathematics Subject Classification: 44A12; 52A38 Remarks: 11 pages The source file(s), GOBR_8_arxiv.tex: 39436 bytes, is(are) stored in gzipped form as 0801.0081.gz with size 14kb. The corresponding postcript file has gzipped size 89kb. Submitted from: borisr at math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0081 or http://arXiv.org/abs/0801.0081 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0081 or in gzipped form by using subject line get 0801.0081 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jan 22 21:43:44 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 450DBD0A7E; Tue, 22 Jan 2008 21:43:44 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Sonja Cox and Mark Veraar Message-Id: <20080123034344.450DBD0A7E at fourier.math.okstate.edu> Date: Tue, 22 Jan 2008 21:43:44 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Some remarks on tangent martingale difference sequences in $L^1$-spaces" by Sonja Cox and Mark Veraar. Abstract: Let $X$ be a Banach space. Suppose that for all $p\in (1, \infty)$ a constant $C_{p,X}$ depending only on $X$ and $p$ exists such that for any two $X$-valued martingales $f$ and $g$ with tangent martingale difference sequences one has \[\E\|f\|^p \leq C_{p,X} \E\|g\|^p \ \ \ \ \ \ (*).\] This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either $f$ or $g$ satisfy the so-called (CI) condition. However, for some applications it suffices to assume that $(*)$ holds whenever $g$ satisfies the (CI) condition. We show that the class of Banach spaces for which $(*)$ holds whenever only $g$ satisfies the (CI) condition is more general than the class of UMD spaces, in particular it includes the space $L^1$. We state several problems related to $(*)$ and other decoupling inequalities. Archive classification: math.PR math.FA Mathematics Subject Classification: 60B05; 46B09; 60G42 Citation: Electron. Commun. Probab. 12, 421-433, (2007) The source file(s), tangent_arxiv.tex: 47306 bytes, is(are) stored in gzipped form as 0801.0695.gz with size 13kb. The corresponding postcript file has gzipped size 101kb. Submitted from: mark at profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0695 or http://arXiv.org/abs/0801.0695 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0695 or in gzipped form by using subject line get 0801.0695 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jan 22 21:48:39 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5E4F8D0A7E; Tue, 22 Jan 2008 21:48:39 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Philippe Jaming, Mate Matolcsi, and Szilard Gy. Revesz Message-Id: <20080123034839.5E4F8D0A7E at fourier.math.okstate.edu> Date: Tue, 22 Jan 2008 21:48:39 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On the extremal rays of the cone of positive, positive definite functions" by Philippe Jaming, Mate Matolcsi, and Szilard Gy. Revesz. Abstract: The aim of this paper is to investigate the cone of non-negative, radial, positive-definite functions in the set of continuous functions on $\R^d$. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article is to characterize some large classes of such extremals. In particular, we show that there many other extremals than the gaussians, thus disproving a conjecture of G. Choquet and that no reasonable conjecture can be made on the full set of extremals. The last feature of this article is to show that many characterizations of positive definite functions available in the literature are actually particular cases of the Choquet integral representations we obtain. Archive classification: math.CA math.FA math.PR Mathematics Subject Classification: 42A82 The source file(s), domain.eps: 12230 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.0941 or http://arXiv.org/abs/0801.0941 or by email in unzipped form by transmitting an empty message with subject line uget 0801.0941 or in gzipped form by using subject line get 0801.0941 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:33:39 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 80BB6D0991; Wed, 6 Feb 2008 08:33:39 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Romain Tessera Message-Id: <20080206143339.80BB6D0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:33:39 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Finding left inverses for classes of operators on l^p(Z^d) with some decay conditions" by Romain Tessera. Abstract: We study the left-invertibility of infinite matrices indexed by metric spaces with polynomial growth. In particular, we consider matrices with polynomial decay, indexed by discrete groups of polynomial growth. Under different conditions on the rows and the columns, we prove that being bounded-below in l^p for some p implies that there is a left-inverse which is bounded in l^q, for all q between 1 and infinity. Archive classification: math.FA Mathematics Subject Classification: 47B38, 47B37 Remarks: 33 pages The source file(s), thinop10.tex: 77101 bytes, is(are) stored in gzipped form as 0801.1532.gz with size 23kb. The corresponding postcript file has gzipped size 163kb. Submitted from: tessera at phare.normalesup.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.1532 or http://arXiv.org/abs/0801.1532 or by email in unzipped form by transmitting an empty message with subject line uget 0801.1532 or in gzipped form by using subject line get 0801.1532 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:35:34 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id EDA12D0991; Wed, 6 Feb 2008 08:35:33 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by V. Valov Message-Id: <20080206143533.EDA12D0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:35:33 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Probability measures and Milyutin maps between metric spaces" by V. Valov. Abstract: We prove that the functor $\Hat{P}$ of Radon probability measures transforms any open map between completely metrizable spaces into a soft map. This result is applied to establish some properties of Milyutin maps between completely metrizable space. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60(primary), 60B05(secondary) Remarks: 14 pages The source file(s), Probability2.tex: 46900 bytes, is(are) stored in gzipped form as 0801.1721.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: veskov at nipissingu.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.1721 or http://arXiv.org/abs/0801.1721 or by email in unzipped form by transmitting an empty message with subject line uget 0801.1721 or in gzipped form by using subject line get 0801.1721 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:37:54 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 7185AD0991; Wed, 6 Feb 2008 08:37:54 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by G. Botelho, M. C. Matos and D. Pellegrino Message-Id: <20080206143754.7185AD0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:37:54 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Lineability of summing sets of homogeneous polynomials" by G. Botelho, M. C. Matos and D. Pellegrino. Abstract: Given a continuous $n$-homogeneous polynomial $P\colon E\longrightarrow F$ between Banach spaces and $1\leq q\leq p<\infty$, in this paper we investigate some properties concerning lineability and spaceability of the $(p;q)$-summing set of $P$, defined by $S_{p;q}(P)=\{a\in E:P\mathrm{~is~}% (p;q)\mathrm{-summing~at~}a\}$. Archive classification: math.FA Mathematics Subject Classification: 46G25 Remarks: 15 pages The source file(s), BotelhoMatosPellegrino.tex: 47676 bytes, is(are) stored in gzipped form as 0801.1812.gz with size 14kb. The corresponding postcript file has gzipped size 100kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.1812 or http://arXiv.org/abs/0801.1812 or by email in unzipped form by transmitting an empty message with subject line uget 0801.1812 or in gzipped form by using subject line get 0801.1812 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:38:57 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9BFF9D0991; Wed, 6 Feb 2008 08:38:57 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marius Junge Message-Id: <20080206143857.9BFF9D0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:38:57 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Noncommutative Riesz transforms I-an algebraic approach" by Marius Junge. Abstract: Riesz transforms on Rn or Riemanian manifolds are classical examples of singular integrals. In this paper we consider Riesz transforms associated to a semigroup Tt of completely positive trace preserving maps on a finite von Neumann algebra. Given a generator A of the semigroup we consider the square of the gradient Gamma(x,y)=A(x^*y)-A(x^*)y-x^*A(y) We prove un upper bound ||\Gamma(x,x)^{1/2}\|_p \le c(p) || (-\Delta)^{1/2}x ||_p under suitable assumptions. These estimates generalizes commutative results by P.A. Meyer, Bakry, Emry, Gundy, Piser. Key tools are square function inequalities obtained in joint work with C. Le Merdy and Q. Xu and new algebraic relations. As an application we obtain new examples of quantum metric spaces for discrete groups with the Haagerup property and rapid decay. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L25 The source file(s), mainfile2.tex: 192365 bytes, is(are) stored in gzipped form as 0801.1873.gz with size 59kb. The corresponding postcript file has gzipped size 283kb. Submitted from: junge at math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.1873 or http://arXiv.org/abs/0801.1873 or by email in unzipped form by transmitting an empty message with subject line uget 0801.1873 or in gzipped form by using subject line get 0801.1873 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:49:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 7F4BFD0991; Wed, 6 Feb 2008 08:49:46 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Geraldo Botelho and Daniel Pellegrino Message-Id: <20080206144946.7F4BFD0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:49:46 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Absolutely summing linear operators into spaces with no finite cotype" by Geraldo Botelho and Daniel Pellegrino. Abstract: Given an infinite-dimensional Banach space $X$ and a Banach space $Y$ with no finite cotype, we determine whether or not every continuous linear operator from $X$ to $Y$ is absolutely $(q;p)$-summing for almost all choices of $p$ and $q$, including the case $p=q$. If $X$ assumes its cotype, the problem is solved for all choices of $p$ and $q$. Applications to the theory of dominated multilinear mappings are also provided. Archive classification: math.FA Mathematics Subject Classification: 47B10 Remarks: 7 pages The source file(s), Botelho-Pellegrino-BullPolish.tex: 22261 bytes, is(are) stored in gzipped form as 0801.2051.gz with size 7kb. The corresponding postcript file has gzipped size 74kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2051 or http://arXiv.org/abs/0801.2051 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2051 or in gzipped form by using subject line get 0801.2051 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:50:39 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id BCCF3D0991; Wed, 6 Feb 2008 08:50:39 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jarno Talponen Message-Id: <20080206145039.BCCF3D0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:50:39 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Operators on C_{0}(L,X) whose range does not contain c_{0}" by Jarno Talponen. Abstract: This paper contains the following results: a) Suppose that X is a non-trivial Banach space and L is a non-empty locally compact Hausdorff space without any isolated points. Then each linear operator T: C_{0}(L,X)\to C_{0}(L,X), whose range does not contain C_{00} isomorphically, satisfies the Daugavet equality ||I+T||=1+||T||. b) Let \Gamma be a non-empty set and X, Y be Banach spaces such that X is reflexive and Y does not contain c_{0} isomorphically. Then any continuous linear operator T: c_{0}(\Gamma,X)\to Y is weakly compact. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B28 The source file(s), dgvt_talponen.tex: 17582 bytes, is(are) stored in gzipped form as 0801.2314.gz with size 6kb. The corresponding postcript file has gzipped size 61kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2314 or http://arXiv.org/abs/0801.2314 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2314 or in gzipped form by using subject line get 0801.2314 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 6 08:51:36 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 00948D0991; Wed, 6 Feb 2008 08:51:35 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jarno Talponen Message-Id: <20080206145136.00948D0991 at fourier.math.okstate.edu> Date: Wed, 6 Feb 2008 08:51:35 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A note on the class of super reflexive almost transitive Banach spaces" by Jarno Talponen. Abstract: The class J of simultaneously almost transitive, uniformly convex and uniformly smooth Banach spaces is characterized in terms of convex-transitivity and weak geometry of the norm. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B20 The source file(s), NoteJ.tex: 21992 bytes, is(are) stored in gzipped form as 0801.2320.gz with size 8kb. The corresponding postcript file has gzipped size 57kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2320 or http://arXiv.org/abs/0801.2320 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2320 or in gzipped form by using subject line get 0801.2320 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:25:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1AFA4D09FA; Tue, 19 Feb 2008 09:25:17 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Yves Dutrieux Gilles Lancien Message-Id: <20080219152517.1AFA4D09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:25:17 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Isometric embeddings of compact spaces into Banach spaces" by Yves Dutrieux Gilles Lancien. Abstract: We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related question: if a Banach space $Y$ contains an isometric copy of the unit ball or of some special compact subset of a separable Banach space $X$, does it necessarily contain a subspace isometric to $X$? We answer positively this question when $X$ is a polyhedral finite-dimensional space, $c_0$ or $\ell_1$. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B20 Remarks: 8 pages The source file(s), dutrieux_lancien.tex: 22590 bytes, is(are) stored in gzipped form as 0801.2486.gz with size 8kb. The corresponding postcript file has gzipped size 79kb. Submitted from: gilles.lancien at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2486 or http://arXiv.org/abs/0801.2486 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2486 or in gzipped form by using subject line get 0801.2486 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:30:57 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 14A39D09FA; Tue, 19 Feb 2008 09:30:56 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jesus Araujo and Juan J. Font Message-Id: <20080219153057.14A39D09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:30:56 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Stability and instability of weighted composition operators" by Jesus Araujo and Juan J. Font. Abstract: Let $\epsilon >0$. A continuous linear operator $T:C(X) \ra C(Y)$ is said to be {\em $\epsilon$-disjointness preserving} if $\vc (Tf)(Tg)\vd_{\infty} \le \epsilon$, whenever $f,g\in C(X)$ satisfy $\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this paper we address basically two main questions: 1.- How close there must be a weighted composition operator to a given $\epsilon$-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given $\epsilon$-disjointness preserving operator? We address these two questions distinguishing among three cases: $X$ infinite, $X$ finite, and $Y$ a singleton ($\epsilon$-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases. Archive classification: math.FA Mathematics Subject Classification: Primary 47B38; Secondary 46J10, 47B33 Remarks: 37 pages, 7 figures. A beamer presentation at www.araujo.tk The source file(s), ejemploy0d.eps: 10802 bytes stability86.tex: 91977 bytes total2gabove.eps: 20323 bytes total2i.eps: 20467 bytes w01c.eps: 9921 bytes w11d.eps: 12594 bytes w21d.eps: 12278 bytes z1d.eps: 12984 bytes, is(are) stored in gzipped form as 0801.2532.tar.gz with size 46kb. The corresponding postcript file has gzipped size 180kb. Submitted from: araujoj at unican.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2532 or http://arXiv.org/abs/0801.2532 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2532 or in gzipped form by using subject line get 0801.2532 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:32:56 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9327AD09FA; Tue, 19 Feb 2008 09:32:56 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by O. Hirzallah, F. Kittaneh, and M. S. Moslehian Message-Id: <20080219153256.9327AD09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:32:56 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Schatten p-norm inequalities related to a characterization of inner product spaces" by O. Hirzallah, F. Kittaneh, and M. S. Moslehian. Abstract: Let $A_1, \cdots A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, \cdots A_n$ belong to a Schatten $p$-class, for some $p>0$, then \begin{equation*} 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. Moreover, \begin{equation*} \sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch. Archive classification: math.OA math.FA Mathematics Subject Classification: 46C15, 47A30, 47B10, 47B15 Remarks: 6 pages The source file(s), Schattenp-norminequalitiesrelatedtoacharacteriztionofinnerproductspaces.tex: 14968 bytes, is(are) stored in gzipped form as 0801.2726.gz with size 4kb. The corresponding postcript file has gzipped size 56kb. Submitted from: moslehian at ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2726 or http://arXiv.org/abs/0801.2726 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2726 or in gzipped form by using subject line get 0801.2726 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:34:07 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id EED7DD09FA; Tue, 19 Feb 2008 09:34:07 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by A. Ibort, P. Linares, and J. G. Llavona Message-Id: <20080219153407.EED7DD09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:34:07 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Continuous multilinear functionals on $C(K)$-spaces are integral" by A. Ibort, P. Linares, and J. G. Llavona. Abstract: In this paper we prove the theorem stated on the title: every continuous multilinear functional on $C(K)$-spaces is integral, or what is the same any polymeasure defined on the product of Borelian $\sigma$-algebras defined on compact sets can be extended to a bounded Borel measure on the compact product space. We provide two different proofs of the same result, each one stressing a different aspect of the various implications of this fact. The first one, valid for compact subsets of $\R^n$, is based on the classical multivariate theory of moments and is a natural extension of the Hausdorff moment problem to multilinear functionals. The second proof relies on a multilinear extension of the decomposition theorem of linear functionals on its positive and negative part which allows us prove a multilinear Riesz Theorem as well. These arguments are valid for arbitrary Hausdorff compact sets. Archive classification: math.FA Mathematics Subject Classification: 46G25 Remarks: 10 pages The source file(s), Integralmultilinear.tex: 39365 bytes, is(are) stored in gzipped form as 0801.2878.gz with size 13kb. The corresponding postcript file has gzipped size 85kb. Submitted from: plinares at mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2878 or http://arXiv.org/abs/0801.2878 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2878 or in gzipped form by using subject line get 0801.2878 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:35:55 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D7456D09FA; Tue, 19 Feb 2008 09:35:55 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann Message-Id: <20080219153555.D7456D09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:35:55 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Majorizing measures and proportional subsets of bounded orthonormal systems" by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann. Abstract: In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any $1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$ such that on $\spa\{\vphi_i\}_{i \in I}$, the $L_1$ norm and the $L_2$ norm are equivalent up to a factor $\mu (\log \mu)^{5/2}$, where $\mu = \sqrt{n/k} \sqrt{\log k}$. The proof is based on a new estimate of the supremum of an empirical process on the unit ball of a Banach space with a good modulus of convexity, via the use of majorizing measures. Archive classification: math.FA math.PR The source file(s), arXiv.tex: 50357 bytes, is(are) stored in gzipped form as 0801.3556.gz with size 16kb. The corresponding postcript file has gzipped size 130kb. Submitted from: alain.pajor at univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.3556 or http://arXiv.org/abs/0801.3556 or by email in unzipped form by transmitting an empty message with subject line uget 0801.3556 or in gzipped form by using subject line get 0801.3556 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:32:56 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9327AD09FA; Tue, 19 Feb 2008 09:32:56 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by O. Hirzallah, F. Kittaneh, and M. S. Moslehian Message-Id: <20080219153256.9327AD09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:32:56 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Schatten p-norm inequalities related to a characterization of inner product spaces" by O. Hirzallah, F. Kittaneh, and M. S. Moslehian. Abstract: Let $A_1, \cdots A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, \cdots A_n$ belong to a Schatten $p$-class, for some $p>0$, then \begin{equation*} 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. Moreover, \begin{equation*} \sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p \end{equation*} for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch. Archive classification: math.OA math.FA Mathematics Subject Classification: 46C15, 47A30, 47B10, 47B15 Remarks: 6 pages The source file(s), Schattenp-norminequalitiesrelatedtoacharacteriztionofinnerproductspaces.tex: 14968 bytes, is(are) stored in gzipped form as 0801.2726.gz with size 4kb. The corresponding postcript file has gzipped size 56kb. Submitted from: moslehian at ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2726 or http://arXiv.org/abs/0801.2726 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2726 or in gzipped form by using subject line get 0801.2726 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:34:07 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id EED7DD09FA; Tue, 19 Feb 2008 09:34:07 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by A. Ibort, P. Linares, and J. G. Llavona Message-Id: <20080219153407.EED7DD09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:34:07 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Continuous multilinear functionals on $C(K)$-spaces are integral" by A. Ibort, P. Linares, and J. G. Llavona. Abstract: In this paper we prove the theorem stated on the title: every continuous multilinear functional on $C(K)$-spaces is integral, or what is the same any polymeasure defined on the product of Borelian $\sigma$-algebras defined on compact sets can be extended to a bounded Borel measure on the compact product space. We provide two different proofs of the same result, each one stressing a different aspect of the various implications of this fact. The first one, valid for compact subsets of $\R^n$, is based on the classical multivariate theory of moments and is a natural extension of the Hausdorff moment problem to multilinear functionals. The second proof relies on a multilinear extension of the decomposition theorem of linear functionals on its positive and negative part which allows us prove a multilinear Riesz Theorem as well. These arguments are valid for arbitrary Hausdorff compact sets. Archive classification: math.FA Mathematics Subject Classification: 46G25 Remarks: 10 pages The source file(s), Integralmultilinear.tex: 39365 bytes, is(are) stored in gzipped form as 0801.2878.gz with size 13kb. The corresponding postcript file has gzipped size 85kb. Submitted from: plinares at mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.2878 or http://arXiv.org/abs/0801.2878 or by email in unzipped form by transmitting an empty message with subject line uget 0801.2878 or in gzipped form by using subject line get 0801.2878 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 19 09:35:55 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D7456D09FA; Tue, 19 Feb 2008 09:35:55 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann Message-Id: <20080219153555.D7456D09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 09:35:55 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Majorizing measures and proportional subsets of bounded orthonormal systems" by Olivier Guedon, Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann. Abstract: In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any $1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$ such that on $\spa\{\vphi_i\}_{i \in I}$, the $L_1$ norm and the $L_2$ norm are equivalent up to a factor $\mu (\log \mu)^{5/2}$, where $\mu = \sqrt{n/k} \sqrt{\log k}$. The proof is based on a new estimate of the supremum of an empirical process on the unit ball of a Banach space with a good modulus of convexity, via the use of majorizing measures. Archive classification: math.FA math.PR The source file(s), arXiv.tex: 50357 bytes, is(are) stored in gzipped form as 0801.3556.gz with size 16kb. The corresponding postcript file has gzipped size 130kb. Submitted from: alain.pajor at univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0801.3556 or http://arXiv.org/abs/0801.3556 or by email in unzipped form by transmitting an empty message with subject line uget 0801.3556 or in gzipped form by using subject line get 0801.3556 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Tue Jan 29 10:23:24 2008 Return-Path: <banach-bounces at math.okstate.edu> Message-Id: <a06230900c3c4f77899e0 at [129.22.117.91]> Date: Tue, 29 Jan 2008 10:40:53 -0500 To: banach at math.okstate.edu From: "Stanislaw J. Szarek" <szarek at cwru.edu> Subject: [Banach] Postdoctoral position at Case Western Reserve University
Department of Mathematics at Case Western Reserve University invites applications for a post-doctoral position starting in the fall of 2008. The position is funded by the NSF Focused Research Group grant "Collaborative Research: Fourier analytic and probabilistic methods in geometric functional analysis and convexity" (see http://www.math.ucdavis.edu/~geofunction). We seek applicants in the area of functional analysis, convexity theory and related high-dimensional phenomena, the direction that recently has been often referred to as ``asymptotic geometric analysis" and of which members of the Department are internationally recognized leaders. See http://www.cwru.edu/artsci/math/szarek/ and http://www.cwru.edu/artsci/math/werner/ for examples of recent research directions. The starting date of the appointment is somewhat flexible, as is the profile: it may involve either 100% effort commitment to the grant (no teaching duties), or an effort split between the grant and teaching (see http://www.case.edu/artsci/math/employment.htm under "Other Searches: Mathematics: Lecturer"). The appointment is initially budgeted for one year, but longer durations under the split effort scenario may be considered. Applicants should submit a letter of application, AMS cover sheet, CV, and have three letters of evaluation sent, preferably by email to math-faculty-position at cwru.edu, with copies to szarek at cwru.edu and elisabeth.werner at case.edu. Applications received by February 15, 2008 will receive full consideration; applications will be accepted until the position is filled. Case is an integral part of one of the major research medical complexes in the country. It also has a major presence in various science and engineering disciplines. Geographically, it is located on the eastern edge of Cleveland, in northeast Ohio, adjacent to University Circle, home to the Cleveland Symphony Orchestra, the Cleveland Museum of Art, and many other cultural institutions. There is a wide variety of housing, schooling, and other amenities nearby. Case Western Reserve University is committed to diversity and is an affirmative action, equal opportunity employer. Applications from women or minorities are especially encouraged. _______________________________________________ Banach mailing list Banach at math.okstate.edu http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Tue Feb 19 10:06:02 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8AB42D09FA; Tue, 19 Feb 2008 10:06:02 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Gilles Pisier Message-Id: <20080219160602.8AB42D09FA at fourier.math.okstate.edu> Date: Tue, 19 Feb 2008 10:06:02 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Complex interpolation between Hilbert, Banach and operator spaces" by Gilles Pisier. Abstract: Motivated by a question of Vincent Lafforgue, we study the Banach spaces $X$ satisfying the following property:\ there is a function $\vp\to \Delta_X(\vp)$ tending to zero with $\vp>0$ such that every operator $T\colon \ L_2\to L_2$ with $\|T\|\le \vp$ that is simultaneously contractive (i.e.\ of norm $\le 1$) on $L_1$ and on $L_\infty$ must be of norm $\le \Delta_X(\vp)$ on $L_2(X)$. We show that $\Delta_X(\vp)\in O(\vp^\alpha)$ for some $\alpha>0$ iff $X$ is isomorphic to a quotient of a subspace of an ultraproduct of $\theta$-Hilbertian spaces for some $ \theta>0$ (see Corollary \ref{comcor4.3}), where $\theta$-Hilbertian is meant in a slightly more general sense than in our previous paper \cite{P1}. Let $B_{{r}}(L_2(\mu))$ be the space of all regular operators on $L_2(\mu)$. We are able to describe the complex interpolation space \[ (B_{{r}}(L_2(\mu), B(L_2(\mu))^\theta. \] We show that $T\colon \ L_2(\mu)\to L_2(\mu)$ belongs to this space iff $T\otimes id_X$ is bounded on $L_2(X)$ for any $\theta$-Hilbertian space $X$. More generally, we are able to describe the spaces $$ (B(\ell_{p_0}), B(\ell_{p_1}))^\theta \ {\rm or}\ (B(L_{p_0}), B(L_{p_1}))^\theta $$ for any pair $1\le p_0,p_1\le \infty$ and $0<\theta<1$. In the same vein, given a locally compact Abelian group $G$, let $M(G)$ (resp.\ $PM(G)$) be the space of complex measures (resp.\ pseudo-measures) on $G$ equipped with the usual norm $\|\mu\|_{M(G)} = |\mu|(G)$ (resp. \[ \|\mu\|_{PM(G)} = \sup\{|\hat\mu(\gamma)| \ \big| \ \gamma\in\widehat G\}). \] We describe similarly the interpolation space $(M(G), PM(G))^\theta$. Various extensions and variants of this result will be given, e.g.\ to Schur multipliers on $B(\ell_2)$ and to operator spaces. Archive classification: math.FA math.OA The source file(s), complex.4fev08.tex: 174268 bytes, is(are) stored in gzipped form as 0802.0476.gz with size 51kb. The corresponding postcript file has gzipped size 253kb. Submitted from: pisier at math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.0476 or http://arXiv.org/abs/0802.0476 or by email in unzipped form by transmitting an empty message with subject line uget 0802.0476 or in gzipped form by using subject line get 0802.0476 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Feb 22 11:23:07 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 25B3AD0A6B; Fri, 22 Feb 2008 11:23:07 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Matthew Neal and Bernard Russo Message-Id: <20080222172307.25B3AD0A6B at fourier.math.okstate.edu> Date: Fri, 22 Feb 2008 11:23:07 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Contractively complemented subspaces of pre-symmetric spaces" by Matthew Neal and Bernard Russo. Abstract: In 1965, Ron Douglas proved that if $X$ is a closed subspace of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$ is the range of a contractive projection on the containing $L^1$-space. In 1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric to another $C_1$-space (possibly finite dimensional), then there is a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved that if a subspace $X$ of the predual of a von Neumann algebra $M$ is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of $M$ onto $X$. We widen significantly the scope of these results by showing that if a subspace $X$ of the predual of a $JBW^*$-triple $A$ is isometric to the predual of another $JBW^*$-triple $B$, then there is a contractive projection on the predual of $A$ with range $X$, as long as $B$ does not have a direct summand which is isometric to a space of the form $L^\infty(\Omega,H)$, where $H$ is a Hilbert space of dimension at least two. The result is false without this restriction on $B$. Archive classification: math.OA math.FA Mathematics Subject Classification: 46B04,46L70,17C65 Remarks: 25 pages The source file(s), ngoz020508.tex: 97855 bytes, is(are) stored in gzipped form as 0802.0734.gz with size 29kb. The corresponding postcript file has gzipped size 155kb. Submitted from: brusso at math.uci.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.0734 or http://arXiv.org/abs/0802.0734 or by email in unzipped form by transmitting an empty message with subject line uget 0802.0734 or in gzipped form by using subject line get 0802.0734 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Feb 22 11:24:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id B5454D0A6B; Fri, 22 Feb 2008 11:24:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Wieslaw Kubis Message-Id: <20080222172429.B5454D0A6B at fourier.math.okstate.edu> Date: Fri, 22 Feb 2008 11:24:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Banach spaces with projectional skeletons" by Wieslaw Kubis. Abstract: A projectional skeleton in a Banach space is a sigma-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to Sigma-spaces. We characterize the existence of a projectional skeleton in terms of elementary substructures, providing simple proofs of known results concerning weakly compactly generated spaces and Plichko spaces. We prove a preservation result for Plichko Banach spaces, involving transfinite sequences of projections. As a corollary, we show that a Banach space is Plichko if and only if it has a commutative projectional skeleton. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26; 46B03; 46E15; 54C35 Remarks: 30 pages (including index and toc), submitted The source file(s), projs_survey-ver2e.bbl: 7090 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.1109 or http://arXiv.org/abs/0802.1109 or by email in unzipped form by transmitting an empty message with subject line uget 0802.1109 or in gzipped form by using subject line get 0802.1109 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Feb 22 11:27:33 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 6D462D0A6B; Fri, 22 Feb 2008 11:27:33 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by D.Karayannakis Message-Id: <20080222172733.6D462D0A6B at fourier.math.okstate.edu> Date: Fri, 22 Feb 2008 11:27:33 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On a conjectured inequality in convex analysis in the case of the unit ball of lp^n" by D.Karayannakis. Abstract: We re-confirm one of the recently stated conjectures of G.Kuperberg of significant convex analysis interest and confirmed very recently for the case of the unit p-ball by A.D.Gutierrez(by use of polygamma functions and convexity theory),this time using only the fundamentals of the gamma function and some mild classical analysis tools. Archive classification: math.CA math.FA Remarks: 4 pages,part of these results comprise a poster to be presented at the 5th Congress of European Mathematics, Amsterdam July 2008 The source file(s), ONACONJECTUREDINEQUALITYINCONVEXANALYSISFORTHECA.pdf: 77405 bytes, is(are) stored in gzipped form as 0802.1942.pdf with size 76kb. Submitted from: dkar at stef.teiher.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.1942 or http://arXiv.org/abs/0802.1942 or by email in unzipped form by transmitting an empty message with subject line uget 0802.1942 or in gzipped form by using subject line get 0802.1942 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Feb 22 11:28:22 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C5DEED0A6B; Fri, 22 Feb 2008 11:28:22 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan Message-Id: <20080222172822.C5DEED0A6B at fourier.math.okstate.edu> Date: Fri, 22 Feb 2008 11:28:22 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Bregman distances and Klee sets" by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan. Abstract: In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version is a famous open problem. In this paper, we consider Klee sets from a new perspective. Rather than measuring distance induced by a norm, we focus on the case when distance is meant in the sense of Bregman, i.e., induced by a convex function. When the convex function has sufficiently nice properties, then - analogously to the Euclidean distance case - every Klee set must be a singleton. We provide two proofs of this result, based on Monotone Operator Theory and on Nonsmooth Analysis. The latter approach leads to results that complement work by Hiriart-Urruty on the Euclidean case. Archive classification: math.FA math.OC Mathematics Subject Classification: 47H05; 41A65; 49J52 The source file(s), submitted.tex: 49600 bytes, is(are) stored in gzipped form as 0802.2322.gz with size 15kb. The corresponding postcript file has gzipped size 113kb. Submitted from: heinz.bauschke at ubc.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.2322 or http://arXiv.org/abs/0802.2322 or by email in unzipped form by transmitting an empty message with subject line uget 0802.2322 or in gzipped form by using subject line get 0802.2322 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Feb 26 08:06:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 82B3ED0A4A; Tue, 26 Feb 2008 08:06:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Yoshimichi Ueda Message-Id: <20080226140629.82B3ED0A4A at fourier.math.okstate.edu> Date: Tue, 26 Feb 2008 08:06:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On peak phenomena for non-commutative $H^\infty$" by Yoshimichi Ueda. Abstract: A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual, and moreover some of the results of Blecher and Labuschagne are generalized to the complete form. Archive classification: math.FA math.OA The source file(s), peak.tex: 31983 bytes, is(are) stored in gzipped form as 0802.3449.gz with size 10kb. The corresponding postcript file has gzipped size 78kb. Submitted from: ueda at math.kyushu-u.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3449 or http://arXiv.org/abs/0802.3449 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3449 or in gzipped form by using subject line get 0802.3449 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 27 09:46:44 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1DDF9D0A7A; Wed, 27 Feb 2008 09:46:44 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Michael Cwikel Message-Id: <20080227154644.1DDF9D0A7A at fourier.math.okstate.edu> Date: Wed, 27 Feb 2008 09:46:44 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Complex interpolation of compact operators mapping into lattice couples" by Michael Cwikel. Abstract: Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and that T is a linear operator which maps A_0 compactly into B_0 and A_1 boundedly (or even compactly) into B_1. Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s compactly for 0<s<1 ? (Here, as usual, [A_0,A_1]_s denotes the complex interpolation space of Alberto Calderon.) This question has been open for 44 years. Affirmative answers are known for it in many special cases. We answer it affirmatively in the case where (A_0,A_1) is arbitrary and (B_0,B_1) is a couple of Banach lattices having absolutely continuous norms or the Fatou property. Archive classification: math.FA Mathematics Subject Classification: 46B70, 46E30 (primary) Remarks: 14 pages. (Page 13 contains routine and standard material which you The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3520 or http://arXiv.org/abs/0802.3520 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3520 or in gzipped form by using subject line get 0802.3520 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 27 09:48:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 72A4BD0A7A; Wed, 27 Feb 2008 09:48:17 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Peng Gao Message-Id: <20080227154817.72A4BD0A7A at fourier.math.okstate.edu> Date: Wed, 27 Feb 2008 09:48:17 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On $l^2$ norms of some weighted mean matrices" by Peng Gao. Abstract: We give another proof of a result of Bennett on the $l^{p}$ operator norms of some weighted mean matrices for the case $p=2$. Archive classification: math.FA Mathematics Subject Classification: 47A30 Remarks: 6 pages The source file(s), Bilinearineqarxiv.tex: 25253 bytes, is(are) stored in gzipped form as 0802.3546.gz with size 7kb. The corresponding postcript file has gzipped size 71kb. Submitted from: penggao at utsc.utoronto.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3546 or http://arXiv.org/abs/0802.3546 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3546 or in gzipped form by using subject line get 0802.3546 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Feb 27 09:49:09 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 48209D0A7A; Wed, 27 Feb 2008 09:49:09 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by M.I. Ostrovskii Message-Id: <20080227154909.48209D0A7A at fourier.math.okstate.edu> Date: Wed, 27 Feb 2008 09:49:09 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Coarse embeddability into Banach spaces" by M.I. Ostrovskii. Abstract: The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into $\ell_2$ implies presence of expander-like structures? (b) To what extent $\ell_2$ is the most difficult space to embed into? Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20; 54E40 Remarks: 23 pages The source file(s), Coarse2007.tex: 46609 bytes, is(are) stored in gzipped form as 0802.3666.gz with size 15kb. The corresponding postcript file has gzipped size 125kb. Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3666 or http://arXiv.org/abs/0802.3666 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3666 or in gzipped form by using subject line get 0802.3666 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Mon Feb 25 17:13:47 2008 Return-Path: <banach-bounces at math.okstate.edu> To: banach at math.okstate.edu Mime-Version: 1.0 Date: Mon, 25 Feb 2008 17:11:51 -0600 From: Dale Alspach <alspach at math.okstate.edu> Subject: [Banach] Lior Tzafriri X-BeenThere: banach at math.okstate.edu X-Mailman-Version: 2.1.9 Precedence: list Reply-To: johnson at math.tamu.edu List-Id: Banach Space Theory News <banach.math.okstate.edu> List-Unsubscribe: <http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=unsubscribe> List-Archive: <http://hardy.math.okstate.edu/pipermail/banach> List-Post: <mailto:banach at math.okstate.edu> List-Help: <mailto:banach-request at math.okstate.edu?subject=help> List-Subscribe: <http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=subscribe> Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: banach-bounces at math.okstate.edu Errors-To: banach-bounces at math.okstate.edu
Lior Tzafriri, Professor Emeritus at the Hebrew University of Jerusalem, died Sunday morning after undergoing heart surgery. Lior had recovered from surgery he underwent in the autumn. He was leading a normal life, going out, frequently coming to the Institute of Mathematics, and was as well humored as usual. Those who knew Lior will miss not only his sharp mathematical insights but his enormous sense of humor, true wisdom, and his gentle behavior that was so surprising for a person with such a strong personality and independence of mind. Lior's funeral will take place 12:00 Tuesday, February 26, at Bet Hahesped, We are very sorry to announce that Professor Lior Tzafriri passed away on February 24, 2008. He died in Jerusalem during an open heart surgery for replacement of a valve in his heart. Lior was born on May 9, 1936 in Bucharest and emigrated to Israel in 1961. He started his university studies in Bucharest but did his PhD in Jerusalem on the subject of spectral operators. He was on the faculty of the Hebrew University since 1970, as a full professor since 1978. He was a visiting professor in several universities, including Northwestern University, University of Minnesota, California Institute of Technology, Cambridge University, University of Copenhagen, IHES, Ohio State University and Texas A&M. Most of his research work was in Banach space theory. Here are some of his contributions to the subject: 1. The solution of the complemented subspaces problem (with J. Lindenstrauss). 2. The structure theory of Orlicz sequence spaces (with J. Lindenstrauss). 3. Spaces with unique unconditional bases up to permutation (with J. Bourgain, P. Casazza and J. Lindenstrauss). 4. The textbooks: Classical Banach Spaces I, II (with J. Lindenstrauss). 5. The 0-2 law (with Y. Katznelson). 6. The structure of Banach spaces with a symmetric structure (with W. B. Johnson, B. Maurey and G. Schechtman). 7. Invertibility of large submatrices (with J. Bourgain). 8. The structure of finite dimensional subspaces of Lp (with J. Bourgain). 9. Work on the Kadison Singer problem (with J. Bourgain). Lior Tzafriri did an outstanding job as the chairman of the Mathematics Department of the Hebrew University during his two separate terms. Those who knew Lior will miss not only his sharp mathematical insights but his enormous sense of humor, true wisdom, and his gentle behavior that was so surprising for a person with such a strong personality and independence of mind. Lior is survived by Marianna, his wife of 51 years; his daughter Edna; his son Rami; and three grandchildren. (Sent by Bill Johnson) _______________________________________________ Banach mailing list Banach at math.okstate.edu http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Fri Feb 29 15:01:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id ACA05D09A1; Fri, 29 Feb 2008 15:01:17 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin Message-Id: <20080229210117.ACA05D09A1 at fourier.math.okstate.edu> Date: Fri, 29 Feb 2008 15:01:17 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The smallest singular value of a random rectangular matrix" by Mark Rudelson and Roman Vershynin. Abstract: We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order \sqrt{N} - \sqrt{n-1} with high probability. A sharp estimate on the probability is also obtained. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52, 11P70 Remarks: 32 pages The source file(s), rv-rectangular-matrices.tex: 80875 bytes, is(are) stored in gzipped form as 0802.3956.gz with size 23kb. The corresponding postcript file has gzipped size 149kb. Submitted from: rudelson at math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3956 or http://arXiv.org/abs/0802.3956 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3956 or in gzipped form by using subject line get 0802.3956 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Mar 4 15:24:44 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 4D685D0A8A; Tue, 4 Mar 2008 15:24:44 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Yun-Su Kim Message-Id: <20080304212444.4D685D0A8A at fourier.math.okstate.edu> Date: Tue, 4 Mar 2008 15:24:44 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Banach Spaces with respect to operator-valued norms" by Yun-Su Kim. Abstract: We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B45 ; 46C07 Remarks: 13 page The source file(s), 2o-Banach.tex: 41954 bytes, is(are) stored in gzipped form as 0803.0041.gz with size 10kb. The corresponding postcript file has gzipped size 83kb. Submitted from: kimys at indiana.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0041 or http://arXiv.org/abs/0803.0041 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0041 or in gzipped form by using subject line get 0803.0041 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 5 11:59:54 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A349BD0A94; Wed, 5 Mar 2008 11:59:54 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jakub Onufry Wojtaszczyk Message-Id: <20080305175954.A349BD0A94 at fourier.math.okstate.edu> Date: Wed, 5 Mar 2008 11:59:54 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A series whose sum range is an arbitrary finite set" by Jakub Onufry Wojtaszczyk. Abstract: In finitely-dimensional spaces the sum range of a series has to be an affine subspace. It is long known this is not the case in infinitely dimensional Banach spaces. In particular in 1984 M.I. Kadets and K. Wo\`{z}niakowski obtained an example of a series the sum range of which consisted of two points, and asked whether it is possible to obtain more than two, but finitely many points. This paper answers the question positively, by showing how to obtain an arbitrary finite set as the sum range of a series in any infinitely dimensional Banach space. Archive classification: math.FA Mathematics Subject Classification: 46B15 Citation: Studia Mathematica 171 (3) (2005), pp. 261-281 Remarks: 21 pages The source file(s), npunktow.tex: 64310 bytes, is(are) stored in gzipped form as 0803.0415.gz with size 20kb. The corresponding postcript file has gzipped size 127kb. Submitted from: onufryw at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0415 or http://arXiv.org/abs/0803.0415 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0415 or in gzipped form by using subject line get 0803.0415 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 5 12:00:44 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 601BAD0A94; Wed, 5 Mar 2008 12:00:44 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jakub Onufry Wojtaszczyk Message-Id: <20080305180044.601BAD0A94 at fourier.math.okstate.edu> Date: Wed, 5 Mar 2008 12:00:44 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The square negative correlation property for generalized Orlicz balls" by Jakub Onufry Wojtaszczyk. Abstract: Antilla, Ball and Perissinaki proved that the squares of coordinate functions in $\ell_p^n$ are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on R^n. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hypothesis for 1-symmetric bodies is given. Currently the CLT is known in full generality for convex bodies (see the paper "Power-law estimates for the central limit theorem for convex sets" by B. Klartag), while for generalized Orlicz balls a much more general result is true (see "The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball" by M. Pilipczuk and J. O. Wojtaszczyk). While, however, both aforementioned papers are rather long, complicated and technical, this paper gives a simple and elementary proof of, eg., the Euclidean concentration for generalized Orlicz balls. Archive classification: math.PR math.FA Mathematics Subject Classification: 52A20, 60D05 Citation: Geometric Aspects of Functional Analysis, Israel Seminar, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0433 or http://arXiv.org/abs/0803.0433 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0433 or in gzipped form by using subject line get 0803.0433 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 5 12:02:09 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8C7A6D0A94; Wed, 5 Mar 2008 12:02:09 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk Message-Id: <20080305180209.8C7A6D0A94 at fourier.math.okstate.edu> Date: Wed, 5 Mar 2008 12:02:09 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball" by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk. Abstract: Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz balls. This allows us to give a strong concentration property, along with a few moment comparison inequalities. Also, the theory of negatively associated variables is being developed in its own right, which allows us to hope more results will be available. Moreover, a simpler proof of a more general result for $\ell_p^n$ balls is given. Archive classification: math.PR math.FA Mathematics Subject Classification: 52A20, 60D05 Remarks: 44 pages (sorry) The source file(s), dlaorlic.tex: 166228 bytes, is(are) stored in gzipped form as 0803.0434.gz with size 46kb. The corresponding postcript file has gzipped size 253kb. Submitted from: onufryw at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0434 or http://arXiv.org/abs/0803.0434 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0434 or in gzipped form by using subject line get 0803.0434 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 5 12:03:25 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E42C4D0A94; Wed, 5 Mar 2008 12:03:25 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by K. J. Swanepoel Message-Id: <20080305180325.E42C4D0A94 at fourier.math.okstate.edu> Date: Wed, 5 Mar 2008 12:03:25 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Vertex degrees of Steiner minimal trees in $\ell_p^d$ and other smooth Minkowski spaces" by K. J. Swanepoel. Abstract: We find upper bounds for the degrees of vertices and Steiner points in Steiner Minimal Trees in the d-dimensional Banach spaces \ell_p^d independent of d. This is in contrast to Minimal Spanning Trees, where the maximum degree of vertices grows exponentially in d (Robins and Salowe, 1995). Our upper bounds follow from characterizations of singularities of SMT's due to Lawlor and Morgan (1994), which we extend, and certain \ell_p-inequalities. We derive a general upper bound of d+1 for the degree of vertices of an SMT in an arbitrary smooth d-dimensional Banach space; the same upper bound for Steiner points having been found by Lawlor and Morgan. We obtain a second upper bound for the degrees of vertices in terms of 1-summing norms. Archive classification: math.MG math.FA Mathematics Subject Classification: 05C05 (Primary); 49Q10 (Secondary) Citation: Discrete & Computational Geometry 21 (1999) 437-447 Remarks: 12 pages The source file(s), steiner-lp.tex: 30143 bytes, is(are) stored in gzipped form as 0803.0443.gz with size 10kb. The corresponding postcript file has gzipped size 81kb. Submitted from: konrad.swanepoel at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0443 or http://arXiv.org/abs/0803.0443 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0443 or in gzipped form by using subject line get 0803.0443 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Tue Mar 11 20:37:10 2008 Return-Path: <banach-bounces at math.okstate.edu> To: banach at math.okstate.edu Date: Tue, 11 Mar 2008 20:36:24 -0500 From: Dale Alspach <alspach at math.okstate.edu> Message-Id: <20080312013624.2BAF7DE58C at szlenk.math.okstate.edu> Subject: [Banach] Workshop in Analysis and Probability Reply-To: johnson at math.tamu.edu List-Id: Banach Space Theory News <banach.math.okstate.edu> List-Unsubscribe: <http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=unsubscribe> List-Archive: <http://hardy.math.okstate.edu/pipermail/banach> List-Post: <mailto:banach at math.okstate.edu> List-Help: <mailto:banach-request at math.okstate.edu?subject=help> List-Subscribe: <http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=subscribe> MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: banach-bounces at math.okstate.edu Errors-To: banach-bounces at math.okstate.edu X-Virus-Scanned: ClamAV using ClamSMTP
Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2008 The Summer 2008 session of the Workshop in Analysis and Probability at Texas A&M University will be in session from July 7 until August 10. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 8-10. Julien Giol <giol at math.tamu.edu>, David Kerr (chair) <kerr at math.tamu.edu>, and Andrew Toms <atoms at mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas at math.tamu.edu> is organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara at math.tamu.edu> or Jaime Vykukal <jaime at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Larson <larson at math.tamu.edu>, Gilles Pisier <pisier at math.tamu.edu>, or Joel Zinn <jzinn at math.tamu.edu>. For information about the Concentration Week "Operator Algebras, Dynamics, and Classification" contact David Kerr <kerr at math.tamu.edu>. For information about the Concentration Week on "Multivariate Operator Theory", contact Ron Douglas <rdouglas at math.tamu.edu>. _______________________________________________ Banach mailing list Banach at math.okstate.edu http://hardy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Fri Mar 14 15:06:40 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 31F08D0595; Fri, 14 Mar 2008 15:06:40 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Manor Mendel and Assaf Naor Message-Id: <20080314200640.31F08D0595 at fourier.math.okstate.edu> Date: Fri, 14 Mar 2008 15:06:40 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Markov convexity and local rigidity of distorted metrics" by Manor Mendel and Assaf Naor. Abstract: The geometry of discrete tree metrics is studied from the following perspectives: 1. Markov p-convexity, which was shown by Lee, Naor, and Peres to be a property of p-convex Banach space, is shown here to be equivalent to p-convexity of Banach spaces. 2. On the other hand, there exists an example of a metric space which is not Markov p-convex for any finite p, but does not uniformly contain complete binary trees. Note that the previous item implies that Banach spaces contain complete binary trees uniformly if and only if they are not Markov p-convex for any finite p. 3. For every B>4, a metric space X is constructed such that all tree metrics can be embedded in X with distortion at most B, but when large complete binary trees are embedded in X, the distortion tends to B. Therefore the class of finite tree metrics do exhibit a dichotomy in the distortions achievable when embedding them in other metric spaces. This is in contrast to the dichotomy exhibited by the class of finite subsets of L_1, and the class of all finite metric spaces. Archive classification: math.MG math.FA Remarks: 10 pages, extended abstract to appear in SoCG '08 %The source file(s), Charlie-tree-socg.bbl: 8435 bytes Charlie-tree-socg.tex: 150202 bytes figs/3path-types.eps: 26109 bytes figs/3path-types.pdf: 13428 bytes figs/d_e-metric.eps: 27160 bytes figs/d_e-metric.pdf: 16009 bytes figs/fork-types.eps: 25081 bytes figs/fork-types.pdf: 12092 bytes figs/lang.eps: 30961 bytes figs/lang.pdf: 14246 bytes figs/mid-lemma1.eps: 18989 bytes figs/mid-lemma1.pdf: 10463 bytes figs/mid-lemma2-c1a.eps: 21267 bytes figs/mid-lemma2-c1a.pdf: 12517 bytes figs/mid-lemma2-c1b.eps: 18219 bytes figs/mid-lemma2-c1b.pdf: 10695 bytes figs/mid-lemma2-c1c.eps: 21626 bytes figs/mid-lemma2-c1c.pdf: 12610 bytes figs/mid-lemma2-c2a.eps: 24273 bytes figs/mid-lemma2-c2a.pdf: 14271 bytes figs/mid-lemma2-c2b.eps: 18207 bytes figs/mid-lemma2-c2b.pdf: 10699 bytes figs/mid-lemma2-c2c.eps: 21237 bytes figs/mid-lemma2-c2c.pdf: 12496 bytes figs/midpoints-new.eps: 17442 bytes figs/midpoints-new.pdf: 9662 bytes figs/tip-contract.eps: 13542 bytes figs/tip-contract.pdf: 6745 bytes figs/type-II-surprise.eps: 17919 bytes figs/type-II-where-w.eps: 11124 bytes sig-alt-full.cls: 56035 bytes, is(are) stored in gzipped form as 0803.1697.tar.gz with size 302kb. The corresponding postcript file has gzipped size 146kb. Submitted from: mendelma at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.1697 or http://arXiv.org/abs/0803.1697 or by email in unzipped form by transmitting an empty message with subject line uget 0803.1697 or in gzipped form by using subject line get 0803.1697 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Mar 21 12:02:16 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 67D00D0540; Fri, 21 Mar 2008 12:02:16 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Ian Doust and Venta Terauds Message-Id: <20080321170216.67D00D0540 at fourier.math.okstate.edu> Date: Fri, 21 Mar 2008 12:02:16 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Extensions of an $AC(\sigma)$ functional calculus" by Ian Doust and Venta Terauds. Abstract: On a reflexive Banach space $X$, if an operator $T$ admits a functional calculus for the absolutely continuous functions on its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an $\AC$ functional calculus is possible for operators acting on families of interpolation spaces such as the $L^p$ spaces. Archive classification: math.FA Mathematics Subject Classification: 47B40 The source file(s), extns-f-submit.tex: 36353 bytes, is(are) stored in gzipped form as 0803.2131.gz with size 11kb. The corresponding postcript file has gzipped size 84kb. Submitted from: i.doust at unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.2131 or http://arXiv.org/abs/0803.2131 or by email in unzipped form by transmitting an empty message with subject line uget 0803.2131 or in gzipped form by using subject line get 0803.2131 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 26 11:59:43 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 34571D05C8; Wed, 26 Mar 2008 11:59:43 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marianne Morillon Message-Id: <20080326165943.34571D05C8 at fourier.math.okstate.edu> Date: Wed, 26 Mar 2008 11:59:43 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Countable choice and compactness" by Marianne Morillon. Abstract: We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p greater or equal to 1 (resp. . p = 0), and some closed subset F of [0, 1]^I which is a bounded subset of l^p(I), we show that AC(N) (resp. DC, the axiom of Dependent Choices) implies the compactness of F. Archive classification: math.FA math.GN math.LO Mathematics Subject Classification: 03E25, 46B26, 54D30 The source file(s), figure.tex: 548 bytes final.bbl: 2612 bytes final.tex: 55144 bytes icone-ermit.eps: 24310 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3131 or http://arXiv.org/abs/0803.3131 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3131 or in gzipped form by using subject line get 0803.3131 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 26 12:00:45 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id B7200D05C8; Wed, 26 Mar 2008 12:00:45 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jarno Talponen Message-Id: <20080326170045.B7200D05C8 at fourier.math.okstate.edu> Date: Wed, 26 Mar 2008 12:00:45 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Lindelof type of generalization of separability in Banach spaces" by Jarno Talponen. Abstract: We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of \mathcal{F}. All separable Banach spaces have CSP and plenty of examples of non-separable CSP spaces are provided. Connections of CSP with Markucevic-bases, Corson property and related geometric issues are discussed. Archive classification: math.FA Mathematics Subject Classification: 46B26; 46A50 The source file(s), csp.tex: 62263 bytes, is(are) stored in gzipped form as 0803.3541.gz with size 17kb. The corresponding postcript file has gzipped size 108kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3541 or http://arXiv.org/abs/0803.3541 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3541 or in gzipped form by using subject line get 0803.3541 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Mar 26 12:01:25 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D849FD05C8; Wed, 26 Mar 2008 12:01:25 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Michael Cwikel Message-Id: <20080326170125.D849FD05C8 at fourier.math.okstate.edu> Date: Wed, 26 Mar 2008 12:01:25 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Lecture notes on duality and interpolation spaces" by Michael Cwikel. Abstract: Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals of his complex interpolation spaces [A_0,A_1]_\theta. The pace is slow, since these notes are intended for graduate students who have just begun to study interpolation spaces. Archive classification: math.FA Mathematics Subject Classification: 46B70 (primary) 46B10 (secondary) Remarks: 24 pages The source file(s), NotesOnDuality-arXiv.tex: 93949 bytes, is(are) stored in gzipped form as 0803.3558.gz with size 25kb. The corresponding postcript file has gzipped size 138kb. Submitted from: mcwikel at math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3558 or http://arXiv.org/abs/0803.3558 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3558 or in gzipped form by using subject line get 0803.3558 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 08:43:25 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 4CB80D090E; Wed, 2 Apr 2008 08:43:25 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Yauhen Radyna, Yakov Radyno, and Anna Sidorik Message-Id: <20080402134325.4CB80D090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 08:43:25 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers" by Yauhen Radyna, Yakov Radyno, and Anna Sidorik. Abstract: We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier transform $F: L_2(Q_p,X)\to L_2(Q_p,X)$ in space of functions, which are square-integrable in Bochner sense and take value in $X$, is a bounded operator. Archive classification: math.FA Mathematics Subject Classification: 46C15, 43A25 Citation: Yauhen Radyna, Yakov Radyno, Anna Sidorik, Characterizing Hilbert The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3646 or http://arXiv.org/abs/0803.3646 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3646 or in gzipped form by using subject line get 0803.3646 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:42:28 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id ADE15D090E; Wed, 2 Apr 2008 09:42:28 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Anton R. Schep Message-Id: <20080402144228.ADE15D090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:42:28 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Products and factors of Banach function spaces" by Anton R. Schep. Abstract: Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E . M(E, F)=F, where M(E,F) denotes the space of multiplication operators from E into F. Archive classification: math.FA Mathematics Subject Classification: 46E30; 47B38 Remarks: 16 pages The source file(s), product-bfs.bbl: 4503 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.4336 or http://arXiv.org/abs/0803.4336 or by email in unzipped form by transmitting an empty message with subject line uget 0803.4336 or in gzipped form by using subject line get 0803.4336 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:43:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1C90ED090E; Wed, 2 Apr 2008 09:43:13 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Th. Schlumprecht and N. Sivakumar Message-Id: <20080402144314.1C90ED090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:43:14 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On the sampling and recovery of bandlimited functions via scattered translates of the Gaussian" by Th. Schlumprecht and N. Sivakumar. Abstract: Let $\lambda$ be a positive number, and let $(x_j:j\in\mathbb Z)\subset\mathbb R$ be a fixed Riesz-basis sequence, namely, $(x_j)$ is strictly increasing, and the set of functions $\{\mathbb R\ni t\mapsto e^{ix_jt}:j\in\mathbb Z\}$ is a Riesz basis ({\it i.e.,\/} unconditionalbasis) for $L_2[-\pi,\pi]$. Given a function $f\in L_2(\mathbb R)$ whose Fourier transform is zero almost everywhere outside the interval $[-\pi,\pi]$, there is a unique square-summable sequence $(a_j:j\in\mathbb Z)$, depending on $\lambda$ and $f$, such that the function$$I_\lambda(f)(x):=\sum_{j\in\mathbb Z}a_je^{-\lambda(x-x_j)^2}, \qquad x\in\mathbb R, $$ is continuous and square integrable on $(-\infty,\infty)$, and satisfies the interpolatory conditions $I_\lambda (f)(x_j)=f(x_j)$, $j\in\mathbb Z$. It is shown that $I_\lambda(f)$ converges to $f$ in $L_2(\mathbb R)$, and also uniformly on $\mathbb R$, as $\lambda\to0^+$. A multidimensional version of this result is also obtained. In addition, the fundamental functions for the univariate interpolation process are defined, and some of their basic properties, including their exponential decay for large argument, are established. It is further shown that the associated interpolation operators are bounded on $\ell_p(\mathbb Z)$ for every $p\in[1,\infty]$. Archive classification: math.CA math.FA Mathematics Subject Classification: 41A05 46E15 The source file(s), scsi1_5.tex: 93892 bytes, is(are) stored in gzipped form as 0803.4344.gz with size 27kb. The corresponding postcript file has gzipped size 165kb. Submitted from: schlump at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.4344 or http://arXiv.org/abs/0803.4344 or by email in unzipped form by transmitting an empty message with subject line uget 0803.4344 or in gzipped form by using subject line get 0803.4344 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:46:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id CC5BAD090E; Wed, 2 Apr 2008 09:46:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Christian Le Merdy and Fedor Sukochev Message-Id: <20080402144605.CC5BAD090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:46:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Rademacher averages on noncommutative symmetric spaces" by Christian Le Merdy and Fedor Sukochev. Abstract: Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let $(\varepsilon_k)_k$ be a Rademacher sequence, on some probability space $\Omega$. For finite sequences $(x_k)_k of E(M), we consider the Rademacher averages $\sum_k \varepsilon_k\otimes x_k$ as elements of the noncommutative function space $E(L^\infty(\Omega)\otimes M)$ and study estimates for their norms $\Vert \sum_k \varepsilon_k \otimes x_k\Vert_E$ calculated in that space. We establish general Khintchine type inequalities in this context. Then we show that if E is 2-concave, the latter norm is equivalent to the infimum of $\Vert (\sum y_k^*y_k)^{\frac{1}{2}}\Vert + \Vert (\sum z_k z_k^*)^{\frac{1}{2}}\Vert$ over all $y_k,z_k$ in E(M) such that $x_k=y_k+z_k$ for any k. Dual estimates are given when E is 2-convex and has a non trivial upper Boyd index. We also study Rademacher averages for doubly indexed families of E(M). Archive classification: math.FA math.OA Mathematics Subject Classification: 46L52; 46M35; 47L05 The source file(s), KHTot.tex: 72248 bytes, is(are) stored in gzipped form as 0803.4404.gz with size 20kb. The corresponding postcript file has gzipped size 152kb. Submitted from: clemerdy at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.4404 or http://arXiv.org/abs/0803.4404 or by email in unzipped form by transmitting an empty message with subject line uget 0803.4404 or in gzipped form by using subject line get 0803.4404 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:47:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id AB981D090E; Wed, 2 Apr 2008 09:47:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Christian Le Merdy, Eric Ricard, and Jean Roydor Message-Id: <20080402144705.AB981D090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:47:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Completely 1-complemented subspaces of Schatten spaces" by Christian Le Merdy, Eric Ricard, and Jean Roydor. Abstract: We consider the Schatten spaces S^p in the framework of operator space theory and for any $1\leq p\not=2<\infty$, we characterize the completely 1-complemented subspaces of S^p. They turn out to be the direct sums of spaces of the form S^p(H,K), where H,K are Hilbert spaces. This result is related to some previous work of Arazy-Friedman giving a description of all 1-complemented subspaces of S^p in terms of the Cartan factors of types 1-4. We use operator space structures on these Cartan factors regarded as subspaces of appropriate noncommutative L^p-spaces. Also we show that for any $n\geq 2$, there is a triple isomorphism on some Cartan factor of type 4 and of dimension 2n which is not completely isometric, and we investigate L^p-versions of such isomorphisms. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L07; 46L89; 17C65 Remarks: To be pubished in the Transactions of the American Mathematical The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.4408 or http://arXiv.org/abs/0803.4408 or by email in unzipped form by transmitting an empty message with subject line uget 0803.4408 or in gzipped form by using subject line get 0803.4408 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:48:16 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A2C61D090E; Wed, 2 Apr 2008 09:48:16 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marius Junge and Christian Le Merdy Message-Id: <20080402144816.A2C61D090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:48:16 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Dilations and rigid factorisations on noncommutative L^p-spaces" by Marius Junge and Christian Le Merdy. Abstract: We study some factorisation and dilation properties of completely positive maps on noncommutative L^p-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (=commutative) L^p-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier's operator space valued noncommutative L^p-spaces that we investigate in the first part of the paper. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L07, 46L51, 48B28 Remarks: To be published in Journal of Functional Analysis The source file(s), JLRevised.tex: 91495 bytes, is(are) stored in gzipped form as 0803.4410.gz with size 26kb. The corresponding postcript file has gzipped size 178kb. Submitted from: clemerdy at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.4410 or http://arXiv.org/abs/0803.4410 or by email in unzipped form by transmitting an empty message with subject line uget 0803.4410 or in gzipped form by using subject line get 0803.4410 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 2 09:49:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E738BD090E; Wed, 2 Apr 2008 09:49:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marianne Morillon Message-Id: <20080402144905.E738BD090E at fourier.math.okstate.edu> Date: Wed, 2 Apr 2008 09:49:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Uniform Eberlein spaces and the finite axiom of choice" by Marianne Morillon. Abstract: We work in set-theory without choice $\ZF$. Given a closed subset $F$ of $[0,1]^I$ which is a bounded subset of $\ell^1(I)$ ({\em resp.} such that $F \subseteq \ell^0(I)$), we show that the countable axiom of choice for finite subsets of $I$, ({\em resp.} the countable axiom of choice $\ACD$) implies that $F$ is compact. This enhances previous results where $\ACD$ ({\em resp.} the axiom of Dependent Choices $\DC$) was required. Moreover, if $I$ is linearly orderable (for example $I=\IR$), the closed unit ball of $\ell^2(I)$ is weakly compact (in $\ZF$). Archive classification: math.FA math.GN math.LO Mathematics Subject Classification: 03E25 , 54B10, 54D30, 46B26 The source file(s), icone-ermit.eps: 24310 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.0154 or http://arXiv.org/abs/0804.0154 or by email in unzipped form by transmitting an empty message with subject line uget 0804.0154 or in gzipped form by using subject line get 0804.0154 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Apr 7 16:44:47 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DFDEDD0AE1; Mon, 7 Apr 2008 16:44:47 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar and L. Weis Message-Id: <20080407214447.DFDEDD0AE1 at fourier.math.okstate.edu> Date: Mon, 7 Apr 2008 16:44:47 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation" by Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar and L. Weis. Abstract: Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation. Archive classification: math.PR math.FA Mathematics Subject Classification: 60H15; 28C20; 35R60; 46B09; 60B11 Remarks: Accepted for publication in Journal of Differential Equations The source file(s), zakai_01_04-2008_arxiv.tex: 83664 bytes, is(are) stored in gzipped form as 0804.0302.gz with size 25kb. The corresponding postcript file has gzipped size 148kb. Submitted from: mark at profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.0302 or http://arXiv.org/abs/0804.0302 or by email in unzipped form by transmitting an empty message with subject line uget 0804.0302 or in gzipped form by using subject line get 0804.0302 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Apr 7 16:45:52 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 13D61D0AE1; Mon, 7 Apr 2008 16:45:51 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Emanuel Milman Message-Id: <20080407214552.13D61D0AE1 at fourier.math.okstate.edu> Date: Mon, 7 Apr 2008 16:45:51 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On the role of convexity in functional and isoperimetric inequalities" by Emanuel Milman. Abstract: This is a continuation of our previous work http://arxiv.org/abs/0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity assumptions (e.g. for log-concave probability measures in Euclidean space), the latter implication can in fact be reversed for very general inequalities, generalizing a reverse form of Cheeger's inequality due to Buser and Ledoux. We develop a coherent single framework for passing between isoperimetric inequalities, Orlicz-Sobolev functional inequalities and capacity inequalities, the latter being notions introduced by Maz'ya and extended by Barthe--Cattiaux--Roberto. As an application, we extend the known results due to the latter authors about the stability of the isoperimetric profile under tensorization, when there is no Central-Limit obstruction. As another application, we show that under our convexity assumptions, $q$-log-Sobolev inequalities ($q \in [1,2]$) are equivalent to an appropriate family of isoperimetric inequalities, extending results of Bakry--Ledoux and Bobkov--Zegarlinski. Our results extend to the more general setting of Riemannian manifolds with density which satisfy the $CD(0,\infty)$ curvature-dimension condition of Bakry--\'Emery. Archive classification: math.FA math.PR Mathematics Subject Classification: 32F32, 26D10, 46E35, 31C15 Remarks: 42 pages The source file(s), Dingir120.eps: 7755 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.0453 or http://arXiv.org/abs/0804.0453 or by email in unzipped form by transmitting an empty message with subject line uget 0804.0453 or in gzipped form by using subject line get 0804.0453 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Apr 7 16:47:06 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A11FAD0AE1; Mon, 7 Apr 2008 16:47:06 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Miroslav Bacak and Petr Hajek Message-Id: <20080407214706.A11FAD0AE1 at fourier.math.okstate.edu> Date: Mon, 7 Apr 2008 16:47:06 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Mazur intersection property for Asplund spaces" by Miroslav Bacak and Petr Hajek. Abstract: The main result of the present note states that it is consistent with the ZFC axioms of set theory (relying on Martin's Maximum MM axiom), that every Asplund space of density character $\om$ has a renorming with the Mazur intersection property. Combined with the previous result of Jim\' enez and Moreno (based upon the work of Kunen under the continuum hypothesis) we obtain that the MIP renormability of Asplund spaces of density $\om$ is undecidable in ZFC. Archive classification: math.FA Mathematics Subject Classification: 46B03 Remarks: 6 pages The source file(s), bacak-hajek.tex: 25023 bytes, is(are) stored in gzipped form as 0804.0583.gz with size 9kb. The corresponding postcript file has gzipped size 70kb. Submitted from: bacak at karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.0583 or http://arXiv.org/abs/0804.0583 or by email in unzipped form by transmitting an empty message with subject line uget 0804.0583 or in gzipped form by using subject line get 0804.0583 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Apr 10 13:43:04 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 86D14D0ADE; Thu, 10 Apr 2008 13:43:04 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by J.M.A.M. van Neerven, M.C. Veraar, and L. Weis Message-Id: <20080410184304.86D14D0ADE at fourier.math.okstate.edu> Date: Thu, 10 Apr 2008 13:43:04 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Stochastic evolution equations in UMD Banach spaces" by J.M.A.M. van Neerven, M.C. Veraar, and L. Weis. Abstract: We discuss existence, uniqueness, and space-time H\"older regularity for solutions of the parabolic stochastic evolution equation \[\left\{\begin{aligned} dU(t) & = (AU(t) + F(t,U(t)))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,\Tend],\\ U(0) & = u_0, \end{aligned} \right. \] where $A$ generates an analytic $C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical Brownian motion with values in a Hilbert space $H$. We prove that if the mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$ satisfy suitable Lipschitz conditions and $u_0$ is $\F_0$-measurable and bounded, then this problem has a unique mild solution, which has trajectories in $C^\l([0,T];\D((-A)^\theta)$ provided $\lambda\ge 0$ and $\theta\ge 0$ satisfy $\l+\theta<\frac12$. Various extensions of this result are given and the results are applied to parabolic stochastic partial differential equations. Archive classification: math.FA math.PR Mathematics Subject Classification: 47D06; 60H15; 28C20; 46B09 Remarks: Accepted for publication in Journal of Functional Analysis The source file(s), scp_arxiv.tex: 157532 bytes, is(are) stored in gzipped form as 0804.0932.gz with size 44kb. The corresponding postcript file has gzipped size 241kb. Submitted from: mark at profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.0932 or http://arXiv.org/abs/0804.0932 or by email in unzipped form by transmitting an empty message with subject line uget 0804.0932 or in gzipped form by using subject line get 0804.0932 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Apr 10 13:45:21 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id CD4FAD0ADE; Thu, 10 Apr 2008 13:45:21 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by William Arveson Message-Id: <20080410184521.CD4FAD0ADE at fourier.math.okstate.edu> Date: Thu, 10 Apr 2008 13:45:21 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Maximal vectors in Hilbert space and quantum entanglement" by William Arveson. Abstract: Given two matrix algebras $M_1$, $M_2$, the natural inclusion of $\mathcal L^1(M_1\otimes M_2)$ in the projective tensor product of Banach spaces $\mathcal L^1(M_1)\hat\otimes \mathcal L^1(M_2)$ is a contraction but not an isometry; and the projective cross norm can be restricted to the convex set $\mathcal S$ of density matrices in $M_1\otimes M_2$to obtain a continuous convex function $E:\mathcal S\to [1,\infty)$. We show that $E$ {\em faithfully measures entanglement} in the sense that a state is entangled if and only if its density matrix $A$ satisfies $E(A)>1$. Moreover, $E(A)$ is maximized at the density matrix $A$ associated with a pure state if and only if the range of $A$ is generated by a maximally entangled unit vector. These concrete results follow from a general analysis of norm-closed subsets $V$ of the unit sphere of a Hilbert space $H$. A {\em maximal vector} (for $V$) is a unit vector $\xi\in H$ whose distance to $V$ is maximum. Maximal vectors generalize the ``maximally entangled" unit vectors of quantum theory. In general, under a mild regularity hypothesis on $V$ we show that there is a {\em norm} on $\mathcal L^1(H)$ whose restriction to the convex set $\mathcal S$ of density operators achieves its minimum precisely on the closed convex hull of the rank one projections associated with vectors in $V$. It achieves its maximum on a rank one projection precisely when its unit vector is a maximal vector. This ``entanglement-measuring norm" is unique, and computation shows it to be the projective cross norm in the above setting of bipartite tensor products $H=H_1\otimes H_2$. Archive classification: math.OA math.FA Mathematics Subject Classification: 46N50,81P68, 94B27 Remarks: 25 pages The source file(s), ent4.tex: 76983 bytes, is(are) stored in gzipped form as 0804.1140.gz with size 21kb. The corresponding postcript file has gzipped size 126kb. Submitted from: arveson at math.berkeley.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.1140 or http://arXiv.org/abs/0804.1140 or by email in unzipped form by transmitting an empty message with subject line uget 0804.1140 or in gzipped form by using subject line get 0804.1140 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Apr 14 09:46:58 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2CDF0D0ADF; Mon, 14 Apr 2008 09:46:58 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Ariel Blanco and Niels Groenbaek Message-Id: <20080414144658.2CDF0D0ADF at fourier.math.okstate.edu> Date: Mon, 14 Apr 2008 09:46:58 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Amenability of algebras of approximable operators" by Ariel Blanco and Niels Groenbaek. Abstract: We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space. Archive classification: math.FA Mathematics Subject Classification: 46B20, 47L10 (primary), 16E40 (secondary) Remarks: 20 pages, to appear in Israel Journal of Mathematics The source file(s), OnAmenability2.tex: 82733 bytes, is(are) stored in gzipped form as 0804.1725.gz with size 25kb. The corresponding postcript file has gzipped size 148kb. Submitted from: gronbaek at math.ku.dk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.1725 or http://arXiv.org/abs/0804.1725 or by email in unzipped form by transmitting an empty message with subject line uget 0804.1725 or in gzipped form by using subject line get 0804.1725 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Apr 15 17:17:21 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 37E4CD0595; Tue, 15 Apr 2008 17:17:21 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Dmitry B. Rokhlin Message-Id: <20080415221721.37E4CD0595 at fourier.math.okstate.edu> Date: Tue, 15 Apr 2008 17:17:21 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Kreps-Yan theorem for Banach ideal spaces" by Dmitry B. Rokhlin. Abstract: Let $C$ be a closed convex cone in a Banach ideal space $X$ on a measurable space with a $\sigma$-finite measure. We prove that conditions $C\cap X_+=\{0\}$ and $C\supset -X_+$ imply the existence of a strictly positive continuous functional on $X$, whose restriction to $C$ is non-positive. Archive classification: math.FA Mathematics Subject Classification: 46E30; 46B42 Remarks: 6 pages The source file(s), RokhlinKreps-Yantheoremforbanachidealspaceseng.tex: 18929 bytes, is(are) stored in gzipped form as 0804.2075.gz with size 7kb. The corresponding postcript file has gzipped size 73kb. Submitted from: rokhlin at math.rsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2075 or http://arXiv.org/abs/0804.2075 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2075 or in gzipped form by using subject line get 0804.2075 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Apr 18 17:10:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 699B8D05DF; Fri, 18 Apr 2008 17:10:14 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Ostrovsky E. Sirota L Message-Id: <20080418221014.699B8D05DF at fourier.math.okstate.edu> Date: Fri, 18 Apr 2008 17:10:14 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Nikol'skii-type inequalities for rearrangement invariant spaces" by Ostrovsky E. Sirota L. Abstract: In this paper we generalize the classical Nikol'skii inequality on the many popular classes pairs of rearrangement invariant (r.i.) spaces and construct some examples in order to show the exactness of our estimations. Archive classification: math.FA Mathematics Subject Classification: 60G17 The source file(s), Nik14_4.tex: 40903 bytes, is(are) stored in gzipped form as 0804.2311.gz with size 14kb. The corresponding postcript file has gzipped size 85kb. Submitted from: leos at post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2311 or http://arXiv.org/abs/0804.2311 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2311 or in gzipped form by using subject line get 0804.2311 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Apr 18 17:11:21 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A5751D05DF; Fri, 18 Apr 2008 17:11:21 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Boris Burshteyn Message-Id: <20080418221121.A5751D05DF at fourier.math.okstate.edu> Date: Fri, 18 Apr 2008 17:11:21 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Uniform lamda-adjustment and mu-approximation in Banach spaces" by Boris Burshteyn. Abstract: We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform lambda-adjustment which is weaker than perturbations by small gap, operator norm, q-norm, and K2-approximation. In arbitrary Banach spaces some of the classical Fredholm stability theorems remain true under uniform lambda-adjustment, while other fail. However, uniformly lambda-adjusted subspaces and linear operators retain their (semi--)Fredholm properties in a Banach space which dual is Fr\'{e}chet-Urysohn in weak* topology. We also introduce another concept of perturbation called uniform mu-approximation which is weaker than perturbations by small gap, norm, and compact convergence, yet stronger than uniform lambda-adjustment. We present Fredholm stability theorems for uniform mu-approximation in arbitrary Banach spaces and a theorem on stability of Riesz kernels and ranges for commuting closed essentially Kato operators. Finally, we define the new concepts of a tuple of subspaces and of a complex of subspaces in Banach spaces, and present stability theorems for index and defect numbers of Fredholm tuples and complexes under uniform lambda-adjustment and uniform mu-approximation. Archive classification: math.FA Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55; 47B07; Remarks: 90 pages The source file(s), boris997paper1.tex: 300886 bytes (looks big), is(are) stored in gzipped form as 0804.2832.gz with size 63kb. The corresponding postcript file has gzipped size 446kb. Submitted from: boris997 at astound.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2832 or http://arXiv.org/abs/0804.2832 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2832 or in gzipped form by using subject line get 0804.2832 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Apr 18 17:12:49 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1A399D05DF; Fri, 18 Apr 2008 17:12:49 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Hirbod Assa Message-Id: <20080418221249.1A399D05DF at fourier.math.okstate.edu> Date: Fri, 18 Apr 2008 17:12:49 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Characterization of compact subsets of $\mathcal{A}^p$ with respect to weak topology" by Hirbod Assa. Abstract: In this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak topology induced by $\mathcal{A}^p$, was recently employed to create the convex risk theory of random processes. The weak compact sets of $\mathcal{A}^p$ are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on $\mathcal{R}^q$ and for their use in the optimization theory. Archive classification: math.PR math.FA Remarks: 8 pages The source file(s), compactsetsAssa.H.tex: 19008 bytes, is(are) stored in gzipped form as 0804.2873.gz with size 6kb. The corresponding postcript file has gzipped size 67kb. Submitted from: assa at dms.umontreal.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2873 or http://arXiv.org/abs/0804.2873 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2873 or in gzipped form by using subject line get 0804.2873 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:00:54 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 29F20D06C7; Wed, 30 Apr 2008 14:00:54 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Dusan Repovs and Pavel V. Semenov Message-Id: <20080430190054.29F20D06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:00:54 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A unified construction yielding precisely Hilbert and James sequences spaces" by Dusan Repovs and Pavel V. Semenov. Abstract: Following James' approach, we shall define the Banach space $J(e)$ for each vector $e=(e_1,e_2,...,e_d) \in \Bbb{R}^d$ with $ e_1 \ne 0$. The construction immediately implies that $J(1)$ coincides with the Hilbert space $i_2$ and that $J(1;-1)$ coincides with the celebrated quasireflexive James space $J$. The results of this paper show that, up to an isomorphism, there are only the following two possibilities: (i) either $J(e)$ is isomorphic to $l_2$ ,if $e_1+e_2+...+e_d\ne 0$ (ii) or $J(e)$ is isomorphic to $J$. Such a dichotomy also holds for every separable Orlicz sequence space $l_M$. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60; 54C65; 41A65; 54C55; 54C20 The source file(s), ArchiveVersion.tex: 21648 bytes, is(are) stored in gzipped form as 0804.3131.gz with size 8kb. The corresponding postcript file has gzipped size 65kb. Submitted from: dusan.repovs at guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3131 or http://arXiv.org/abs/0804.3131 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3131 or in gzipped form by using subject line get 0804.3131 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:02:12 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 53215D06C7; Wed, 30 Apr 2008 14:02:12 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Mark Veraar and Tuomas Hytonen Message-Id: <20080430190212.53215D06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:02:12 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "R-boundedness of smooth operator-valued functions" by Mark Veraar and Tuomas Hytonen. Abstract: In this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the first part we show that certain integral operator are $R$-bounded. This will be used to obtain $R$-boundedness in the case that $\mathcal{T}$ is the range of an operator-valued function $T:\R^d\to \calL(X,Y)$ which is in a certain Besov space $B^{d/r}_{r,1}(\R^d;\calL(X,Y))$. The results will be applied to obtain $R$-boundedness of semigroups and evolution families, and to obtain sufficient conditions for existence of solutions for stochastic Cauchy problems. Archive classification: math.FA math.PR Mathematics Subject Classification: 47B99; 46B09; 46E35; 46E40 The source file(s), rboundedsmooth_arxiv.tex: 81153 bytes, is(are) stored in gzipped form as 0804.3313.gz with size 24kb. The corresponding postcript file has gzipped size 142kb. Submitted from: mark at profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3313 or http://arXiv.org/abs/0804.3313 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3313 or in gzipped form by using subject line get 0804.3313 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:03:02 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C9FEDD06C7; Wed, 30 Apr 2008 14:03:02 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Venta Terauds Message-Id: <20080430190302.C9FEDD06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:03:02 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Functional calculus extensions on dual spaces" by Venta Terauds. Abstract: In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one. Archive classification: math.FA Mathematics Subject Classification: 47B40 Remarks: 7 pages The source file(s), func_calc_extns_terauds.tex: 24129 bytes, is(are) stored in gzipped form as 0804.3451.gz with size 7kb. The corresponding postcript file has gzipped size 70kb. Submitted from: venta.terauds at newcastle.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3451 or http://arXiv.org/abs/0804.3451 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3451 or in gzipped form by using subject line get 0804.3451 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:30:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 3662CD06C7; Wed, 30 Apr 2008 14:30:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Matthew Daws, Hung Le Pham and Stuart White Message-Id: <20080430193005.3662CD06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:30:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" by Matthew Daws, Hung Le Pham and Stuart White. Abstract: We investigate possible preduals of the measure algebra $M(G)$ of a locally compact group and the Fourier algebra $A(G)$ of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak$^*$-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals $C_0(G)$ of $M(G)$ and $C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a natural coassociative multiplication and show that the canonical predual gives rise to the unique weak$^*$-topology making both the multiplication separately weak$^*$-continuous and the coassociative multiplication weak$^*$-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure. Archive classification: math.FA math.OA Mathematics Subject Classification: 43A20, 43A77 Remarks: 21 pages The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are) stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding postcript file has gzipped size 133kb. Submitted from: matt.daws at cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3764 or http://arXiv.org/abs/0804.3764 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3764 or in gzipped form by using subject line get 0804.3764 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:31:36 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E6D7BD06C7; Wed, 30 Apr 2008 14:31:36 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Andrea Colesanti and Eugenia Saorin-Gomez Message-Id: <20080430193136.E6D7BD06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:31:36 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals" by Andrea Colesanti and Eugenia Saorin-Gomez. Abstract: We use Brunn-Minkowski inequalities for quermassintegrals to deduce a family of inequalities of Poincar\'e type on the unit sphere and on the boundary of smooth convex bodies in the $n$-dimensional Euclidean space. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20; 26D10 Remarks: 15 pages The source file(s), cs3.tex: 37802 bytes, is(are) stored in gzipped form as 0804.3867.gz with size 12kb. The corresponding postcript file has gzipped size 109kb. Submitted from: colesant at math.unifi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3867 or http://arXiv.org/abs/0804.3867 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3867 or in gzipped form by using subject line get 0804.3867 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:33:04 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 72DF4D06C7; Wed, 30 Apr 2008 14:33:04 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jarno Talponen Message-Id: <20080430193304.72DF4D06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:33:04 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The isometry group of L^{p}(\mu,\X) is SOT-contractible" by Jarno Talponen. Abstract: We will show that if (\Omega,\Sigma,\mu) is an atomless positive measure space, X is a Banach space and 1\leq p<\infty, then the group of isometric automorphisms on the Bochner space L^{p}(\mu,X) is contractible in the strong operator topology. We do not require \Sigma or X above to be separable. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B25; 46E40 The source file(s), contr32.tex: 27449 bytes, is(are) stored in gzipped form as 0804.4427.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.4427 or http://arXiv.org/abs/0804.4427 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4427 or in gzipped form by using subject line get 0804.4427 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Apr 30 14:34:58 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9155DD06C7; Wed, 30 Apr 2008 14:34:58 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Michael Doree, Olga Maleva Message-Id: <20080430193458.9155DD06C7 at fourier.math.okstate.edu> Date: Wed, 30 Apr 2008 14:34:58 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A compact null set containing a differentiability point of every Lipschitz function" by Michael Doree and Olga Maleva. Abstract: We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly. Archive classification: math.FA math.CA Mathematics Subject Classification: 46G05; 46T20 Remarks: 31 pages The source file(s), DoreMaleva.tex: 76535 bytes, is(are) stored in gzipped form as 0804.4576.gz with size 22kb. The corresponding postcript file has gzipped size 144kb. Submitted from: o.maleva at warwick.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.4576 or http://arXiv.org/abs/0804.4576 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4576 or in gzipped form by using subject line get 0804.4576 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Mon May 5 13:09:06 2008 Return-Path: <banach-bounces at math.okstate.edu> To: banach at math.okstate.edu Date: Mon, 05 May 2008 07:46:24 -0500 From: Dale Alspach <alspach at math.okstate.edu> Subject: [Banach] symposium
On May 27-28 the Institute of Mathematics of the Hebrew University of Jerusalem is organizing a memorial symposium for Lior Tzafriri, titled "Geometry of Banach Spaces". A tentative program of the symposium can be found on the webpage: http://www.ma.huji.ac.il/~landau/conf/banach_08.html _______________________________________________ Banach mailing list Banach at math.okstate.edu https://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Tue May 13 10:41:18 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C2714D06D5; Tue, 13 May 2008 10:41:18 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Oscar Blasco and Sandra Pott Message-Id: <20080513154118.C2714D06D5 at fourier.math.okstate.edu> Date: Tue, 13 May 2008 10:41:18 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Embeddings between operator-valued dyadic BMO spaces" by Oscar Blasco and Sandra Pott. Abstract: We investigate a scale of dyadic operator-valued BMO spaces, corresponding to the different yet equivalent characterizations of dyadic BMO in the scalar case. In the language of operator spaces, we investigate different operator space structures on the scalar dyadic BMO space which arise naturally from the different characterisations of scalar BMO. We also give sharp dimensional growth estimates for the sweep of functions and its bilinear extension in some of those different dyadic BMO spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 42B30, 42B35, Secondary 47B35 Remarks: to appear in Illinois J. Math The source file(s), BlascoPott2.tex: 45114 bytes, is(are) stored in gzipped form as 0805.0620.gz with size 14kb. The corresponding postcript file has gzipped size 102kb. Submitted from: s.pott at maths.gla.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.0620 or http://arXiv.org/abs/0805.0620 or by email in unzipped form by transmitting an empty message with subject line uget 0805.0620 or in gzipped form by using subject line get 0805.0620 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 15 17:35:47 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 55773D07E8; Thu, 15 May 2008 17:35:47 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pandelis Dodos, Jordi Lopez Abad and Stevo Todorcevic Message-Id: <20080515223547.55773D07E8 at fourier.math.okstate.edu> Date: Thu, 15 May 2008 17:35:47 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Unconditional basic sequences in spaces of large density" by Pandelis Dodos, Jordi Lopez Abad and Stevo Todorcevic. Abstract: We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement that every Banach space of density $\aleph_\omega$ contains an unconditional basic sequence. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B03, 03E35 The source file(s), DLT.tex: 74305 bytes, is(are) stored in gzipped form as 0805.1860.gz with size 22kb. The corresponding postcript file has gzipped size 136kb. Submitted from: abad at logique.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.1860 or http://arXiv.org/abs/0805.1860 or by email in unzipped form by transmitting an empty message with subject line uget 0805.1860 or in gzipped form by using subject line get 0805.1860 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 15 17:36:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C75D2D07E8; Thu, 15 May 2008 17:36:29 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pandelis Dodos Message-Id: <20080515223629.C75D2D07E8 at fourier.math.okstate.edu> Date: Thu, 15 May 2008 17:36:29 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Definability under duality" by Pandelis Dodos. Abstract: It is shown that if $A$ is an analytic class of separable Banach spaces with separable dual, then the set $A^*=\{ Y:\exists X\in A \text{ with } Y\cong X^*\}$ is analytic. The corresponding result for pre-duals is false. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B10 Remarks: 9 pages, no figures The source file(s), DualsVersion-ArXiv.tex: 29048 bytes, is(are) stored in gzipped form as 0805.2036.gz with size 9kb. The corresponding postcript file has gzipped size 79kb. Submitted from: pdodos at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2036 or http://arXiv.org/abs/0805.2036 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2036 or in gzipped form by using subject line get 0805.2036 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 15 17:37:09 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id CE492D07E8; Thu, 15 May 2008 17:37:09 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pandelis Dodos Message-Id: <20080515223709.CE492D07E8 at fourier.math.okstate.edu> Date: Thu, 15 May 2008 17:37:09 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On antichains of spreading models of Banach spaces" by Pandelis Dodos. Abstract: We show that for every separable Banach space $X$, either $\spw(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\spw(X)$ contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell and B. Sari. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B20 Remarks: 14 pages, no figures. Canadian Mathematical Bulletin (to appear) The source file(s), SP-ArXiv.tex: 44752 bytes, is(are) stored in gzipped form as 0805.2038.gz with size 13kb. The corresponding postcript file has gzipped size 96kb. Submitted from: pdodos at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2038 or http://arXiv.org/abs/0805.2038 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2038 or in gzipped form by using subject line get 0805.2038 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 15 17:38:18 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 6E6C2D07E8; Thu, 15 May 2008 17:38:18 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pandelis Dodos Message-Id: <20080515223818.6E6C2D07E8 at fourier.math.okstate.edu> Date: Thu, 15 May 2008 17:38:18 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On classes of Banach spaces admitting ``small" universal spaces" by Pandelis Dodos. Abstract: We characterize those classes $\ccc$ of separable Banach spaces admitting a separable universal space $Y$ (that is, a space $Y$ containing, up to isomorphism, all members of $\ccc$) which is not universal for all separable Banach spaces. The characterization is a byproduct of the fact, proved in the paper, that the class $\mathrm{NU}$ of non-universal separable Banach spaces is strongly bounded. This settles in the affirmative the main conjecture form \cite{AD}. Our approach is based, among others, on a construction of $\llll_\infty$-spaces, due to J. Bourgain and G. Pisier. As a consequence we show that there exists a family $\{Y_\xi:\xi<\omega_1\}$ of separable, non-universal, $\llll_\infty$-spaces which uniformly exhausts all separable Banach spaces. A number of other natural classes of separable Banach spaces are shown to be strongly bounded as well. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15 Remarks: 25 pages, no figures The source file(s), Universal-ArXiv.tex: 81806 bytes, is(are) stored in gzipped form as 0805.2043.gz with size 24kb. The corresponding postcript file has gzipped size 143kb. Submitted from: pdodos at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2043 or http://arXiv.org/abs/0805.2043 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2043 or in gzipped form by using subject line get 0805.2043 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 15 17:39:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2A177D07E8; Thu, 15 May 2008 17:39:14 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pandelis Dodos and Jordi Lopez-Abad Message-Id: <20080515223914.2A177D07E8 at fourier.math.okstate.edu> Date: Thu, 15 May 2008 17:39:14 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On unconditionally saturated Banach spaces" by Pandelis Dodos and Jordi Lopez-Abad. Abstract: We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$, of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space $Y$, with a Schauder basis, that contains isomorphic copies of every space $X$ in the class $\aaa$. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15 Remarks: 16 pages, no figures. Studia Mathematica (to appear) The source file(s), UnconditionallySaturated-ArXiv.tex: 49281 bytes, is(are) stored in gzipped form as 0805.2046.gz with size 14kb. The corresponding postcript file has gzipped size 102kb. Submitted from: pdodos at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2046 or http://arXiv.org/abs/0805.2046 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2046 or in gzipped form by using subject line get 0805.2046 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue May 27 13:30:56 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id AA84DD07D3; Tue, 27 May 2008 13:30:56 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Isabelle Chalendar, Emmanuel Fricain, and Dan Timotin Message-Id: <20080527183056.AA84DD07D3 at fourier.math.okstate.edu> Date: Tue, 27 May 2008 13:30:56 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A note on James spaces and superstrictly singular operators" by Isabelle Chalendar, Emmanuel Fricain, and Dan Timotin. Abstract: An elementary lemma is used in order to show that the natural inclusion $J_p\to J_q$ of James spaces is superstrictly singular for $p<q$. As a consequence, it is shown that an operator without nontrivial invariant subspaces constructed by Charles Read is superstrictly singular. Archive classification: math.FA The source file(s), James.tex: 20594 bytes, is(are) stored in gzipped form as 0805.3409.gz with size 7kb. The corresponding postcript file has gzipped size 70kb. Submitted from: fricain at math.univ-lyon1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3409 or http://arXiv.org/abs/0805.3409 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3409 or in gzipped form by using subject line get 0805.3409 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue May 27 13:37:28 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C240BD07D3; Tue, 27 May 2008 13:37:28 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Mark Rudelson and Roman Vershynin Message-Id: <20080527183728.C240BD07D3 at fourier.math.okstate.edu> Date: Tue, 27 May 2008 13:37:28 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The least singular value of a random square matrix is O(n^{-1/2})" by Mark Rudelson and Roman Vershynin. Abstract: Let A be a matrix whose entries are real i.i.d. centered random variables with unit variance and suitable moment assumptions. Then the smallest singular value of A is of order n^{-1/2} with high probability. The lower estimate of this type was proved recently by the authors; in this note we establish the matching upper estimate. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52 Remarks: 6 pages The source file(s), square-matrices-reverse.tex: 17210 bytes, is(are) stored in gzipped form as 0805.3407.gz with size 6kb. The corresponding postcript file has gzipped size 68kb. Submitted from: vershynin at math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3407 or http://arXiv.org/abs/0805.3407 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3407 or in gzipped form by using subject line get 0805.3407 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue May 27 13:38:35 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D4466D07D3; Tue, 27 May 2008 13:38:35 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Fernando Rambla Jarno Talponen Message-Id: <20080527183835.D4466D07D3 at fourier.math.okstate.edu> Date: Tue, 27 May 2008 13:38:35 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Simultaneous realization of function space structures in transitive Banach spaces" by Fernando Rambla and Jarno Talponen. Abstract: Let L be a locally compact Hausdorff space and m the Lebesgue measure on the unit interval. We will prove the existence of a transitive Banach space X such that C_{0}(L,X) and the Bochner spaces L^{p}(m,X), 1\leq p\leq \infty, are all isometrically isomorphic to X. Also, more general results of this type are presented. Added note:THIS PAPER WAS WITHDRAWN May 29, 2008 Archive classification: math.FA Mathematics Subject Classification: 46B04; 46E40 The source file(s), BCO4.tex: 52768 bytes, is(are) stored in gzipped form as 0805.3616.gz with size 15kb. The corresponding postcript file has gzipped size 96kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3616 or http://arXiv.org/abs/0805.3616 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3616 or in gzipped form by using subject line get 0805.3616 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue May 27 13:39:45 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 26EDDD07D3; Tue, 27 May 2008 13:39:45 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann Message-Id: <20080527183945.26EDDD07D3 at fourier.math.okstate.edu> Date: Tue, 27 May 2008 13:39:45 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On the nontrivial projection problem" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann. Abstract: The Nontrivial Projection Problem asks whether every finite-dimensional normed space of dimension greater than one admits a well-bounded projection of non-trivial rank and corank or, equivalently, whether every centrally symmetric convex body (of arbitrary dimension greater than one) is approximately affinely equivalent to a direct product of two bodies of non-trivial dimension. We show that this is true "up to a logarithmic factor." Archive classification: math.FA Mathematics Subject Classification: 46B20, secondary 46B07, 52A21 Remarks: 17 pages The source file(s), NPPforArxiv.tex: 46100 bytes, is(are) stored in gzipped form as 0805.3792.gz with size 17kb. The corresponding postcript file has gzipped size 126kb. Submitted from: szarek at cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3792 or http://arXiv.org/abs/0805.3792 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3792 or in gzipped form by using subject line get 0805.3792 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue May 27 13:40:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2915AD07D3; Tue, 27 May 2008 13:40:46 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Chao You and Bao Qi Feng Message-Id: <20080527184046.2915AD07D3 at fourier.math.okstate.edu> Date: Tue, 27 May 2008 13:40:46 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On distribution and almost convergence of bounded sequences" by Chao You and Bao Qi Feng. Abstract: In this paper, we give the concepts of properly distributed and simply distributed sequences, and prove that they are almost convergent. Basing on these, we review the work of Feng and Li [Feng, B. Q. and Li, J. L., Some estimations of Banach limits, J. Math. Anal. Appl. 323(2006) No. 1, 481-496. MR2262220 46B45 (46A45).], which is shown to be a special case of our generalized theory. Archive classification: math.FA math.GM Mathematics Subject Classification: Primary 40G05, 46A35, 54A20; Secondary 11K36 Remarks: 8 pages The source file(s), Ondistributionandalmostconvergenceofboundedsequences.tex: 25039 bytes, is(are) stored in gzipped form as 0805.3950.gz with size 8kb. The corresponding postcript file has gzipped size 68kb. Submitted from: hityou1982 at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3950 or http://arXiv.org/abs/0805.3950 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3950 or in gzipped form by using subject line get 0805.3950 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu May 29 12:12:38 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8383BD06A5; Thu, 29 May 2008 12:12:38 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Craig Calcaterra and Axel Boldt Message-Id: <20080529171238.8383BD06A5 at fourier.math.okstate.edu> Date: Thu, 29 May 2008 12:12:38 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Approximating with Gaussians" by Craig Calcaterra and Axel Boldt. Abstract: Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares. Taking the Fourier transform of this result shows low-frequency trigonometric series are dense in L^2 with Gaussian weight function. Archive classification: math.CA math.FA Mathematics Subject Classification: 41A30; 42A32; 42C10 Remarks: 16 pages, 23 figures The source file(s), AppGaussArXiv3.tex: 61111 bytes I100.png: 14299 bytes I200.png: 7466 bytes I210.png: 8594 bytes I220.png: 8450 bytes I230.png: 9254 bytes I240.png: 8799 bytes I250.png: 8967 bytes I300.png: 8446 bytes I310.png: 10845 bytes I311.png: 10945 bytes I320.png: 10846 bytes I330.png: 11696 bytes I340.png: 11710 bytes I350.png: 11061 bytes I400.png: 10444 bytes I410.png: 10145 bytes I420.png: 9810 bytes I500.png: 10246 bytes I510.png: 10478 bytes I520.png: 11634 bytes I530.png: 11233 bytes I600.png: 10241 bytes I610.png: 11497 bytes, is(are) stored in gzipped form as 0805.3795.tar.gz with size 202kb. The corresponding postcript file has gzipped size 279kb. Submitted from: axel.boldt at metrostate.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.3795 or http://arXiv.org/abs/0805.3795 or by email in unzipped form by transmitting an empty message with subject line uget 0805.3795 or in gzipped form by using subject line get 0805.3795 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:24:16 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E0BBFD081B; Tue, 3 Jun 2008 22:24:13 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by D. Drivaliaris and N. Yannakakis Message-Id: <20080604032414.E0BBFD081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:24:13 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Subspaces with a common complement in a Banach space" by D. Drivaliaris and N. Yannakakis. Abstract: We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution S on X exchanging the two subspaces, such that I+S is bounded from below on their union. Moreover we show that, in a separable Hilbert space, the only pairs of subspaces with a common complement are those which are either equivalently positioned or not completely asymptotic to one another. We also obtain characterizations for the existence of a common complement for subspaces with closed sum. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46C05; 47A05 Citation: Studia Mathematica 182 (2) (2007), 141-164 The source file(s), common_arxiv.tex: 74237 bytes, is(are) stored in gzipped form as 0805.4707.gz with size 16kb. The corresponding postcript file has gzipped size 104kb. Submitted from: d.drivaliaris at fme.aegean.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4707 or http://arXiv.org/abs/0805.4707 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4707 or in gzipped form by using subject line get 0805.4707 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:26:09 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F122AD081B; Tue, 3 Jun 2008 22:26:07 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by D. Drivaliaris and N. Yannakakis Message-Id: <20080604032608.F122AD081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:26:07 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Hilbert space structure and positive operators" by D. Drivaliaris and N. Yannakakis. Abstract: Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially complemented subspace which is isomorphic to a Hilbert space. We also treat the non-symmetric case. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46C15; 47B99 Citation: Journal of Mathematical Analysis and Applications 305 (2) (2005), The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4721 or http://arXiv.org/abs/0805.4721 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4721 or in gzipped form by using subject line get 0805.4721 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:28:08 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 551B3D081B; Tue, 3 Jun 2008 22:28:08 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Markus Biegert Message-Id: <20080604032808.551B3D081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:28:08 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Lattice homomorphisms between Sobolev spaces" by Markus Biegert. Abstract: We show that every vector lattice homomorphism $T$ from $W^{1,p}_0(\Omega_1)$ into $W^{1,q}(\Omega_2)$ for $p,q\in (1,\infty)$ and open sets \Omega_1,\Omega_2\subset\IR^N$ has a representation of the form $Tu=(u\circ\xi)g\quad\mbox{ $\Cap_q$-quasi everywhere on }\Omega_2$ with mappings $\xi:\Omega_2\to\Omega_1$ and $g:\Omega_2\to[0,\infty)$. This representation follows as an application of an abstract and more general representation theorem, which can be applied in many other situations. We prove that every lattice homomorphism $T$ from $\tsW^{1,p}(\Omega_1)$ into $W^{1,q}(\Omega_2)$ admits a representation of the form $Tu=(u\circ\xi)g\quad\mbox{ $\Cap_q$-quasi everywhere on }\Omega_2$ with mappings $\xi:\Omega_2\to\overline\Omega_1$ and $g:\Omega_2\to[0,\infty)$. Here $\tsW^{1,p}(\Omega_1)$ denotes the closure of $W^{1,p}(\Omega_1)\cap C_c(\overline\Omega_1)$ in $W^{1,p}(\Omega_1)$ and every $u\in\tsW^{1,p}(\Omega_1)$ admits a trace on the boundary $\partial\Omega_1$ of $\Omega_1$. Finally we prove that every lattice homomorphism $T$ from $\tsW^{1,p}(\Omega_1)$ into $\tsW^{1,q}(\Omega_2)$ where $\Omega_1$ is bounded has a representation of the form $Tu=(u\circ\xi)g\quad\mbox{ $\Cap_{q,\Omega_2}$-quasi everywhere on }\overline\Omega_2$ with mappings $\xi:\overline\Omega_2\to\overline\Omega_1$ and $g:\overline\Omega_2\to[0,\infty)$. At the end of this article we consider also lattice isomorphisms between Sobolev spaces and the representation of their inverses. Archive classification: math.AP math.FA The source file(s), orderhomomorphism.bbl: 4468 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.4740 or http://arXiv.org/abs/0805.4740 or by email in unzipped form by transmitting an empty message with subject line uget 0805.4740 or in gzipped form by using subject line get 0805.4740 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:29:45 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C5837D081B; Tue, 3 Jun 2008 22:29:45 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Joaquim Martin and Mario Milman Message-Id: <20080604032945.C5837D081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:29:45 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Isometry and symmetrization for logarithmic Sobolev inequalities" by Joaquim Martin and Mario Milman. Abstract: Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts. Archive classification: math.FA math.AP The source file(s), Gauss-final-rev.tex: 69485 bytes, is(are) stored in gzipped form as 0806.0021.gz with size 19kb. The corresponding postcript file has gzipped size 129kb. Submitted from: mario.milman at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.0021 or http://arXiv.org/abs/0806.0021 or by email in unzipped form by transmitting an empty message with subject line uget 0806.0021 or in gzipped form by using subject line get 0806.0021 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:32:42 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 98C4AD081B; Tue, 3 Jun 2008 22:32:40 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Hamed Hatami Message-Id: <20080604033242.98C4AD081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:32:40 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Graph norms and Sidorenko's conjecture" by Hamed Hatami. Abstract: Let $H$ and $G$ be two finite graphs. Define $h_H(G)$ to be the number of homomorphisms from $H$ to $G$. The function $h_H(\cdot)$ extends in a natural way to a function from the set of symmetric matrices to $\mathbb{R}$ such that for $A_G$, the adjacency matrix of a graph $G$, we have $h_H(A_G)=h_H(G)$. Let $m$ be the number of edges of $H$. It is easy to see that when $H$ is the cycle of length $2n$, then $h_H(\cdot)^{1/m}$ is the $2n$-th Schatten-von Neumann norm. We investigate a question of Lov\'{a}sz that asks for a characterization of graphs $H$ for which the function $h_H(\cdot)^{1/m}$ is a norm. We prove that $h_H(\cdot)^{1/m}$ is a norm if and only if a H\"{o}lder type inequality holds for $H$. We use this inequality to prove both positive and negative results, showing that $h_H(\cdot)^{1/m}$ is a norm for certain classes of graphs, and giving some necessary conditions on the structure of $H$ when $h_H(\cdot)^{1/m}$ is a norm. As an application we use the inequality to verify a conjecture of Sidorenko for certain graphs including hypercubes. In fact for such graphs we can prove statements that are much stronger than the assertion of Sidorenko's conjecture. We also investigate the $h_H(\cdot)^{1/m}$ norms from a Banach space theoretic point of view, determining their moduli of smoothness and convexity. This generalizes the previously known result for the $2n$-th Schatten-von Neumann norms. Archive classification: math.FA math.CO Mathematics Subject Classification: 46E30; 05C35 Remarks: to appear in Israel Journal of Mathematics The source file(s), arxiv/normFinal.bbl: 6949 bytes arxiv/normFinal.tex: 57888 bytes arxiv/normFinal.toc: 1082 bytes, is(are) stored in gzipped form as 0806.0047.tar.gz with size 20kb. The corresponding postcript file has gzipped size 125kb. Submitted from: hamed at cs.toronto.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.0047 or http://arXiv.org/abs/0806.0047 or by email in unzipped form by transmitting an empty message with subject line uget 0806.0047 or in gzipped form by using subject line get 0806.0047 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:34:36 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E1E5FD081B; Tue, 3 Jun 2008 22:34:36 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by G. Androulakis and K. Beanland Message-Id: <20080604033436.E1E5FD081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:34:36 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Descriptive set theoretic methods applied to strictly singular and strictly cosingular operators" by G. Androulakis and K. Beanland. Abstract: The class of strictly singular operators originating from the dual of a separable Banach space is written as an increasing union of $\omega_1$ subclasses which are defined using the Schreier sets. A question of J. Diestel, of whether a similar result can be stated for strictly cosingular operators, is studied. Archive classification: math.FA Mathematics Subject Classification: 47B07, 47A15 The source file(s), AlmostSC.tex: 41247 bytes, is(are) stored in gzipped form as 0806.0056.gz with size 12kb. The corresponding postcript file has gzipped size 95kb. Submitted from: giorgis at math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.0056 or http://arXiv.org/abs/0806.0056 or by email in unzipped form by transmitting an empty message with subject line uget 0806.0056 or in gzipped form by using subject line get 0806.0056 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jun 3 22:36:28 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 4351ED081B; Tue, 3 Jun 2008 22:36:28 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by G. Androulakis, S. J. Dilworth, and N. J. Kalton Message-Id: <20080604033628.4351ED081B at fourier.math.okstate.edu> Date: Tue, 3 Jun 2008 22:36:28 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces" by G. Androulakis, S. J. Dilworth, and N. J. Kalton. Abstract: We give a new approach to the Ramsey-type results of Gowers on block bases in Banach spaces and apply our results to prove the Gowers dichotomy in F-spaces. Archive classification: math.FA Mathematics Subject Classification: 46A16, 91A05, 91A80 The source file(s), AndDilKal.tex: 70671 bytes, is(are) stored in gzipped form as 0806.0058.gz with size 20kb. The corresponding postcript file has gzipped size 132kb. Submitted from: giorgis at math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.0058 or http://arXiv.org/abs/0806.0058 or by email in unzipped form by transmitting an empty message with subject line uget 0806.0058 or in gzipped form by using subject line get 0806.0058 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Jun 4 07:43:51 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DBFD3D05E7; Wed, 4 Jun 2008 07:43:51 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jaegil Kim and Han Ju Lee Message-Id: <20080604124351.DBFD3D05E7 at fourier.math.okstate.edu> Date: Wed, 4 Jun 2008 07:43:51 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices" by Jaegil Kim and Han Ju Lee. Abstract: Using the variational method, it is shown that the set of all strong peak functions in a closed algebra $A$ of $C_b(K)$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space $X$ is a norming subset of $\mathcal{P}({}^n X)$, then the set of all strongly norm attaining elements in $\mathcal{P}({}^n X)$ is dense. In particular, the set of all points at which the norm of $\mathcal{P}({}^n X)$ is Fr\'echet differentiable is a dense $G_\delta$ subset. In the last part, using Reisner's graph theoretic-approach, we construct some strongly norm attaining polynomials on a CL-space with an absolute norm. Then we show that for a finite dimensional complex Banach space $X$ with an absolute norm, its polynomial numerical indices are one if and only if $X$ is isometric to $\ell_\infty^n$. Moreover, we give a characterization of the set of all complex extreme points of the unit ball of a CL-space with an absolute norm. Archive classification: math.FA math.CO Mathematics Subject Classification: 46G25; 46B20; 46B22; 52A21; 46B20 The source file(s), graph-June3-08.tex: 54865 bytes, is(are) stored in gzipped form as 0806.0507.gz with size 15kb. The corresponding postcript file has gzipped size 117kb. Submitted from: hahnju at postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.0507 or http://arXiv.org/abs/0806.0507 or by email in unzipped form by transmitting an empty message with subject line uget 0806.0507 or in gzipped form by using subject line get 0806.0507 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Tue Jun 17 16:36:00 2008 Return-Path: <banach-bounces at math.okstate.edu> Date: Tue, 17 Jun 2008 15:24:59 -0500 (CDT) From: Bill Johnson <johnson at math.tamu.edu> To: banach at math.okstate.edu Message-ID: <Pine.LNX.4.64.0806171523110.17874 at fourier.math.tamu.edu> MIME-Version: 1.0 X-Virus-Scanned: ClamAV using ClamSMTP X-Mailman-Approved-At: Tue, 17 Jun 2008 16:35:20 -0500 Content-Disposition: attachment; filename=SUMIRFAS08.1.txt X-Content-Filtered-By: Mailman/MimeDel 2.1.9 Subject: [Banach] SUMIRFAS 2008 X-BeenThere: banach at math.okstate.edu X-Mailman-Version: 2.1.9 Precedence: list List-Id: Banach Space Theory News <banach.math.okstate.edu> List-Unsubscribe: <https://mail.math.okstate.edu/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=unsubscribe> List-Archive: <http://mail.math.okstate.edu/pipermail/banach> List-Post: <mailto:banach at math.okstate.edu> List-Help: <mailto:banach-request at math.okstate.edu?subject=help> List-Subscribe: <https://mail.math.okstate.edu/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=subscribe> Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: banach-bounces at math.okstate.edu Errors-To: banach-bounces at math.okstate.edu X-Virus-Scanned: ClamAV using ClamSMTP
1st ANNOUNCEMENT OF SUMIRFAS 2008 The Informal Regional Functional Analysis Seminar August 8 - 10 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 155. Plenary speakers at SUMIRFAS 2008 include Bill Arveson, Nate Brown, Ron DeVore, Nicole Tomczak-Jaegermann, and Elisabeth Werner. Gideon Schechtman, and Joel Zinn, are organizing a Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena" that will take place August 6 - August 10. The first day will be devoted to introductory talks designed to introduce non experts to the subject. Julien Giol <giol at math.tamu.edu>, David Kerr (chair) <kerr at math.tamu.edu>, and Andrew Toms <atoms at mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas at math.tamu.edu> and Jaydeb Sarkar <jsarkar at math.tamu.edu> are organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. For more information, please visit URL http://www.math.tamu.edu/~jsarkar/cowmot.html. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell them if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical support, please contact Cara Barton, cara at math.tamu.edu. For more information on the Workshop itself, please contact William Johnson, johnson at math.tamu.edu, David Larson, larson at math.tamu.edu, Gilles Pisier, pisier at math.tamu.edu, or Joel Zinn, jzinn at math.tamu.edu. For information about the Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena", please contact Joel Zinn, jzinn at math.tamu.edu. _______________________________________________ Banach mailing list Banach at math.okstate.edu https://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Wed Jun 18 14:56:08 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 884A4D0809; Wed, 18 Jun 2008 14:56:08 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Vladimir Kadets, Varvara Shepelska and Dirk Werner Message-Id: <20080618195608.884A4D0809 at fourier.math.okstate.edu> Date: Wed, 18 Jun 2008 14:56:08 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Quotients of Banach spaces with the Daugavet property" by Vladimir Kadets, Varvara Shepelska and Dirk Werner. Abstract: We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues for narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ over an $\ell_1$-subspace can fail the Daugavet property. The latter answers a question posed to us by A. Pelczynski in the negative. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B25; 47B38 Remarks: 15 pages The source file(s), dpry_bullpol_june08.tex: 55217 bytes, is(are) stored in gzipped form as 0806.1815.gz with size 17kb. The corresponding postcript file has gzipped size 114kb. Submitted from: werner at math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.1815 or http://arXiv.org/abs/0806.1815 or by email in unzipped form by transmitting an empty message with subject line uget 0806.1815 or in gzipped form by using subject line get 0806.1815 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jul 1 13:34:37 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C8A41D0838; Tue, 1 Jul 2008 13:34:36 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazzaa Message-Id: <20080701183436.C8A41D0838 at fourier.math.okstate.edu> Date: Tue, 1 Jul 2008 13:34:36 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A criterion of weak compactness for operators on subspaces of Orlicz spaces" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazzaa. Abstract: To appear in J. Funct. Spaces and Appl. Archive classification: math.FA Mathematics Subject Classification: 46E30 Remarks: 18 pages The source file(s), critere.tex: 40456 bytes, is(are) stored in gzipped form as 0806.4204.gz with size 13kb. The corresponding postcript file has gzipped size 97kb. Submitted from: lefevre at euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4204 or http://arXiv.org/abs/0806.4204 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4204 or in gzipped form by using subject line get 0806.4204 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jul 1 13:37:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8F18ED0838; Tue, 1 Jul 2008 13:37:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Joel A. Tropp Message-Id: <20080701183705.8F18ED0838 at fourier.math.okstate.edu> Date: Tue, 1 Jul 2008 13:37:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Column subset selection, matrix factorization, and eigenvalue optimization" by Joel A. Tropp. Abstract: Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing {\sf QR}, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains another strand of work on column selection whose algorithmic implications have not been explored. In particular, a celebrated result of Bourgain and Tzafriri demonstrates that each matrix with normalized columns contains a large column submatrix that is exceptionally well conditioned. Unfortunately, standard proofs of this result cannot be regarded as algorithmic. This paper presents a randomized, polynomial-time algorithm that produces the submatrix promised by Bourgain and Tzafriri. The method involves random sampling of columns, followed by a matrix factorization that exposes the well-conditioned subset of columns. This factorization, which is due to Grothendieck, is regarded as a central tool in modern functional analysis. The primary novelty in this work is an algorithm, based on eigenvalue minimization, for constructing the Grothendieck factorization. These ideas also result in a novel approximation algorithm for the $(\infty, 1)$ norm of a matrix, which is generally {\sf NP}-hard to compute exactly. As an added bonus, this work reveals a surprising connection between matrix factorization and the famous {\sc maxcut} semidefinite program. Archive classification: math.NA math.FA Mathematics Subject Classification: 15A60; 15A23; 65F30; 90C25 Remarks: Conference version The source file(s), alg.sty: 7607 bytes macro-file.tex: 8456 bytes subset-selection-soda-v4.bbl: 4536 bytes subset-selection-soda-v4.tex: 88398 bytes, is(are) stored in gzipped %form as 0806.4404.tar.gz with size 30kb. The corresponding postcript file has gzipped size 109kb. Submitted from: jtropp at acm.caltech.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4404 or http://arXiv.org/abs/0806.4404 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4404 or in gzipped form by using subject line get 0806.4404 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Jul 1 13:38:22 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id BD44BD0838; Tue, 1 Jul 2008 13:38:22 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Konrad J. Swanepoel Message-Id: <20080701183822.BD44BD0838 at fourier.math.okstate.edu> Date: Tue, 1 Jul 2008 13:38:22 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Simultaneous packing and covering in sequence spaces" by Konrad J. Swanepoel. Abstract: We adapt a construction of Klee (1981) to find a packing of unit balls in $\ell_p$ ($1\leq p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20 (primary), 52C17 (secondary) Remarks: 5 pages The source file(s), klee.tex: 14156 bytes, is(are) stored in gzipped form as 0806.4473.gz with size 5kb. The corresponding postcript file has gzipped size 92kb. Submitted from: konrad.swanepoel at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0806.4473 or http://arXiv.org/abs/0806.4473 or by email in unzipped form by transmitting an empty message with subject line uget 0806.4473 or in gzipped form by using subject line get 0806.4473 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 10 15:12:39 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5A643D051F; Thu, 10 Jul 2008 15:12:39 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Greg Kuperberg Message-Id: <20080710201239.5A643D051F at fourier.math.okstate.edu> Date: Thu, 10 Jul 2008 15:12:39 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "From the Mahler conjecture to Gauss linking integrals" by Greg Kuperberg. Abstract: We establish a version of the bottleneck conjecture, which in turn implies a partial solution to the Mahler conjecture on the product $v(K) = (\Vol K)(\Vol K^\circ)$ of the volume of a symmetric convex body $K \in \R^n$ and its polar body $K^\circ$. The Mahler conjecture asserts that the Mahler volume $v(K)$ is minimized (non-uniquely) when $K$ is an $n$-cube. The bottleneck conjecture (in its least general form) asserts that the volume of a certain domain $K^\diamond \subseteq K \times K^\circ$ is minimized when $K$ is an ellipsoid. It implies the Mahler conjecture up to a factor of $(\pi/4)^n \gamma_n$, where $\gamma_n$ is a monotonic factor that begins at $4/\pi$ and converges to $\sqrt{2}$. This strengthens a result of Bourgain and Milman, who showed that there is a constant $c$ such that the Mahler conjecture is true up to a factor of $c^n$. The proof uses a version of the Gauss linking integral to obtain a constant lower bound on $\Vol K^\diamond$, with equality when $K$ is an ellipsoid. It applies to a more general conjecture concerning the join of any two necks of the pseudospheres of an indefinite inner product space. Because the calculations are similar, we will also analyze traditional Gauss linking integrals in the sphere $S^{n-1}$ and in hyperbolic space $H^{n-1}$. Archive classification: math.MG math.DG math.FA Remarks: 10 pages, 4 figures. Dedicated to my father, on no particular The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math/0610904 or http://arXiv.org/abs/math/0610904 or by email in unzipped form by transmitting an empty message with subject line uget math/0610904 or in gzipped form by using subject line get math/0610904 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 10 15:13:37 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DB3DDD051F; Thu, 10 Jul 2008 15:13:37 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marisa Zymonopoulou Message-Id: <20080710201337.DB3DDD051F at fourier.math.okstate.edu> Date: Thu, 10 Jul 2008 15:13:37 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The modified complex Busemann-Petty problem on sections of convex bodies" by Marisa Zymonopoulou. Abstract: Since the answer to the complex Busemann-Petty problem is negative in most dimensions, it is natural to ask what conditions on the (n-1)-dimensional volumes of the central sections of complex convex bodies with complex hyperplanes allow to compare the n-dimensional volumes. In this article we give necessary conditions on the section function in order to obtain an affirmative answer in all dimensions. Archive classification: math.FA The source file(s), MCBP.tex: 44421 bytes, is(are) stored in gzipped form as 0807.0776.gz with size 12kb. The corresponding postcript file has gzipped size 104kb. Submitted from: marisa at math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0776 or http://arXiv.org/abs/0807.0776 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0776 or in gzipped form by using subject line get 0807.0776 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 10 15:14:27 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 36E75D051F; Thu, 10 Jul 2008 15:14:27 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marisa Zymonopoulou Message-Id: <20080710201427.36E75D051F at fourier.math.okstate.edu> Date: Thu, 10 Jul 2008 15:14:27 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The complex Busemann-Petty problem for arbitrary measures" by Marisa Zymonopoulou. Abstract: The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n\leq 3 and negative if n\geq 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" arbitrary measure. This result is the complex analogue of Zvavitch's generalization to arbitrary measures of the original real Busemann-Petty problem. Archive classification: math.FA The source file(s), CBPGM.tex: 37275 bytes, is(are) stored in gzipped form as 0807.0779.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: marisa at math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.0779 or http://arXiv.org/abs/0807.0779 or by email in unzipped form by transmitting an empty message with subject line uget 0807.0779 or in gzipped form by using subject line get 0807.0779 to: math at arXiv.org.
From banach-bounces at math.okstate.edu Thu Jul 10 15:09:24 2008 Return-Path: <banach-bounces at math.okstate.edu> X-Spam-Checker-Version: SpamAssassin 3.2.5 (2008-06-10) on szlenk.math.okstate.edu X-Spam-Level: X-Spam-Status: No, score=-2.6 required=5.0 tests=AWL,BAYES_00 autolearn=ham version=3.2.5 X-Original-To: alspach at localhost Delivered-To: alspach at localhost Received: from szlenk.math.okstate.edu (localhost [127.0.0.1]) by szlenk.math.okstate.edu (Postfix) with ESMTP id 1F5D5DF76F for <alspach at localhost>; Thu, 10 Jul 2008 15:09:24 -0500 (CDT) X-Original-To: alspach at math.okstate.edu Delivered-To: alspach at math.okstate.edu Received: from hardy.math.okstate.edu [139.78.112.2] by szlenk.math.okstate.edu with IMAP (fetchmail-6.3.8) for <alspach at localhost> (single-drop); Thu, 10 Jul 2008 15:09:24 -0500 (CDT) Received: from mail.math.okstate.edu (localhost.localdomain [127.0.0.1]) by mail.math.okstate.edu (Postfix) with ESMTP id 14E2BF009D; Thu, 10 Jul 2008 15:07:53 -0500 (CDT) Received: by mail.math.okstate.edu (Postfix, from userid 110) id B1C06F00B6; Thu, 10 Jul 2008 15:07:52 -0500 (CDT) Received: from hardy.math.okstate.edu (localhost.localdomain [127.0.0.1]) by mail.math.okstate.edu (Postfix) with ESMTP id 14660F009D; Thu, 10 Jul 2008 15:07:38 -0500 (CDT) X-Original-To: banach at math.okstate.edu Delivered-To: banach at math.okstate.edu Received: from mail.math.okstate.edu (localhost.localdomain [127.0.0.1]) by mail.math.okstate.edu (Postfix) with ESMTP id 12AEDF0091 for <banach at math.okstate.edu>; Thu, 10 Jul 2008 13:36:10 -0500 (CDT) Received: by mail.math.okstate.edu (Postfix, from userid 110) id EF7CCF00AD; Thu, 10 Jul 2008 13:36:09 -0500 (CDT) Received: from radon.math.tamu.edu (radon.math.tamu.edu [165.91.100.16]) by mail.math.okstate.edu (Postfix) with ESMTP id 64801F0091 for <banach at math.okstate.edu>; Thu, 10 Jul 2008 13:35:57 -0500 (CDT) Received: from fourier.math.tamu.edu (fourier.math.tamu.edu [165.91.100.14]) by radon.math.tamu.edu (Postfix) with ESMTP id 0D84231C0A9 for <banach at math.okstate.edu>; Thu, 10 Jul 2008 13:35:57 -0500 (CDT) Received: by fourier.math.tamu.edu (Postfix, from userid 121) id D35544866BA; Thu, 10 Jul 2008 13:35:56 -0500 (CDT) Received: from localhost (localhost [127.0.0.1]) by fourier.math.tamu.edu (Postfix) with ESMTP id AE38E4865F1 for <banach at math.okstate.edu>; Thu, 10 Jul 2008 13:35:56 -0500 (CDT) Date: Thu, 10 Jul 2008 13:35:56 -0500 (CDT) From: Bill Johnson <johnson at math.tamu.edu> To: banach at math.okstate.edu Message-ID: <Pine.LNX.4.64.0807101334130.13225 at fourier.math.tamu.edu> MIME-Version: 1.0 X-Virus-Scanned: ClamAV using ClamSMTP X-Mailman-Approved-At: Thu, 10 Jul 2008 15:07:35 -0500 Subject: [Banach] SUMIRFAS-2nd announcement X-BeenThere: banach at math.okstate.edu X-Mailman-Version: 2.1.9 Precedence: list List-Id: Banach Space Theory News <banach.math.okstate.edu> List-Unsubscribe: <https://mail.math.okstate.edu/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=unsubscribe> List-Archive: <http://mail.math.okstate.edu/pipermail/banach> List-Post: <mailto:banach at math.okstate.edu> List-Help: <mailto:banach-request at math.okstate.edu?subject=help> List-Subscribe: <https://mail.math.okstate.edu/mailman/listinfo/banach>, <mailto:banach-request at math.okstate.edu?subject=subscribe> Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Sender: banach-bounces at math.okstate.edu Errors-To: banach-bounces at math.okstate.edu X-Virus-Scanned: ClamAV using ClamSMTP
2nd ANNOUNCEMENT OF SUMIRFAS 2008 The Informal Regional Functional Analysis Seminar August 8 - 10 Texas A&M University, College Station Confirmed speakers and titles are given below. The schedule for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 165. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 155. Julien Giol <giol at math.tamu.edu>, David Kerr (chair) <kerr at math.tamu.edu>, and Andrew Toms <atoms at mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas at math.tamu.edu> and Jaydeb Sarkar <jsarkar at math.tamu.edu> are organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. For more information, please visit URL http://www.math.tamu.edu/~jsarkar/cowmot.html. On Saturday evening there will be a BBQ at the home of Jan and Bill Johnson. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell them if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical support, please contact Cara Barton, cara at math.tamu.edu. For more information on the Workshop itself, please contact William Johnson, johnson at math.tamu.edu, David Larson, larson at math.tamu.edu, Gilles Pisier, pisier at math.tamu.edu, or Joel Zinn, jzinn at math.tamu.edu. Speakers include: Bill Arveson, Maximal vectors in Hilbert space and quantum entanglement Nate Brown, Hilbert modules and the Cuntz semigroup Marius Dadarlat, Finite dimensional approximations of amenable groups Ron DeVore, A Taste of Compressed Sensing Detelin Dosev, Commutators on certain Banach spaces Constanze Liaw, Singular integrals and rank one perturbations Timur Oikhberg, The complexity of the complete isomorphism relation between subspaces of an operator space (joint work with C. Rosendal) Grigoris Paouris, Small ball probability estimates for log-concave measures Chris Phillips, Freeness of actions of finite groups on C*-algebras Bunyamin Sari, On uniform classification of the direct sums of $\ell_p$-spaces Nicole Tomczak-Jaegermann, Random embeddings and other high-dimensional geometric phenomena Elisabeth Werner, Orlicz functions and minima and maxima of random variables _______________________________________________ Banach mailing list Banach at math.okstate.edu https://mail.math.okstate.edu/mailman/listinfo/banach
From alspach at fourier.math.okstate.edu Thu Jul 17 15:03:09 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 6CE90D0869; Thu, 17 Jul 2008 15:03:08 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by William B. Johnson and Assaf Naor Message-Id: <20080717200308.6CE90D0869 at fourier.math.okstate.edu> Date: Thu, 17 Jul 2008 15:03:08 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite" by William B. Johnson and Assaf Naor. Abstract: Let $X$ be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer $n$ and any $x_1,\ldots,x_n\in X$ there exists a linear mapping $L:X\to F$, where $F\subseteq X$ is a linear subspace of dimension $O(\log n)$, such that $\|x_i-x_j\|\le\|L(x_i)-L(x_j)\|\le O(1)\cdot\|x_i-x_j\|$ for all $i,j\in \{1,\ldots, n\}$. We show that this implies that $X$ is almost Euclidean in the following sense: Every $n$-dimensional subspace of $X$ embeds into Hilbert space with distortion $2^{2^{O(\log^*n)}}$. On the other hand, we show that there exists a normed space $Y$ which satisfies the J-L lemma, but for every $n$ there exists an $n$-dimensional subspace $E_n\subseteq Y$ whose Euclidean distortion is at least $2^{\Omega(\alpha(n))}$, where $\alpha$ is the inverse Ackermann function. Archive classification: math.FA math.MG The source file(s), JL-L3.1.TEX: 43297 bytes, is(are) stored in gzipped form as 0807.1919.gz with size 14kb. The corresponding postcript file has gzipped size 74kb. Submitted from: naor at cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.1919 or http://arXiv.org/abs/0807.1919 or by email in unzipped form by transmitting an empty message with subject line uget 0807.1919 or in gzipped form by using subject line get 0807.1919 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 17 15:05:21 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1ED5ED0869; Thu, 17 Jul 2008 15:05:21 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Christian Rosendal Message-Id: <20080717200521.1ED5ED0869 at fourier.math.okstate.edu> Date: Thu, 17 Jul 2008 15:05:21 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "An exact Ramsey principle for block sequences" by Christian Rosendal. Abstract: We prove an exact, i.e., formulated without $\Delta$-expansions, Ramsey principle for infinite block sequences in vector spaces over countable fields, where the two sides of the dichotomic principle are represented by respectively winning strategies in Gowers' block sequence game and winning strategies in the infinite asymptotic game. This allows us to recover Gowers' dichotomy theorem for block sequences in normed vector spaces by a simple application of the basic determinacy theorem for infinite asymptotic games. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B03, 03E15 The source file(s), ExactRamseyPrinciples17submitted.tex: 37130 bytes, is(are) stored in gzipped form as 0807.2205.gz with size 11kb. The corresponding postcript file has gzipped size 82kb. Submitted from: rosendal at math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2205 or http://arXiv.org/abs/0807.2205 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2205 or in gzipped form by using subject line get 0807.2205 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 17 15:06:52 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id CDC86D0869; Thu, 17 Jul 2008 15:06:52 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias Message-Id: <20080717200652.CDC86D0869 at fourier.math.okstate.edu> Date: Thu, 17 Jul 2008 15:06:52 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Strictly singular non-compact diagonal operators on HI spaces" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias. Abstract: We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$. \end{abstract} Archive classification: math.FA Mathematics Subject Classification: 46B28, 46B20, 46B03 The source file(s), diagonal_adt_1.tex: 147103 bytes, is(are) stored in gzipped form as 0807.2388.gz with size 39kb. The corresponding postcript file has gzipped size 213kb. Submitted from: sargyros at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2388 or http://arXiv.org/abs/0807.2388 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2388 or in gzipped form by using subject line get 0807.2388 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Jul 17 15:08:49 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 33B75D0869; Thu, 17 Jul 2008 15:08:49 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Spiros A. Argyros, Alexander D. Arvanitakis, and Andreas G. Tolias Message-Id: <20080717200849.33B75D0869 at fourier.math.okstate.edu> Date: Thu, 17 Jul 2008 15:08:49 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Saturated extensions, the attractors method and Hereditarily James Tree Space" by Spiros A. Argyros, Alexander D. Arvanitakis, and Andreas G. Tolias. Abstract: In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors. Archive classification: math.FA The source file(s), Aat6.tex: 290045 bytes, is(are) stored in gzipped form as 0807.2392.gz with size 77kb. The corresponding postcript file has gzipped size 377kb. Submitted from: sargyros at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2392 or http://arXiv.org/abs/0807.2392 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2392 or in gzipped form by using subject line get 0807.2392 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Jul 23 13:07:26 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 3C446D086E; Wed, 23 Jul 2008 13:07:26 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Anthony Weston Message-Id: <20080723180726.3C446D086E at fourier.math.okstate.edu> Date: Wed, 23 Jul 2008 13:07:26 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Optimal lower bounds on the maximal p-negative type of finite metric spaces" by Anthony Weston. Abstract: This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric space. Examples show that these lower bounds can easily be best possible under clearly delineated circumstances. We further point out that the entire theory holds (more generally) for finite semi-metric spaces without modification and wherein the lower bounds are always optimal. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20 Remarks: 10 pages The source file(s), Gap.tex: 36066 bytes, is(are) stored in gzipped form as 0807.2705.gz with size 11kb. The corresponding postcript file has gzipped size 95kb. Submitted from: westona at canisius.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2705 or http://arXiv.org/abs/0807.2705 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2705 or in gzipped form by using subject line get 0807.2705 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Jul 23 13:08:01 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1F1CED086E; Wed, 23 Jul 2008 13:08:01 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Hermann Pfitzner Message-Id: <20080723180801.1F1CED086E at fourier.math.okstate.edu> Date: Wed, 23 Jul 2008 13:08:01 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Boundaries for Banach spaces determine weak compactness" by Hermann Pfitzner. Abstract: A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that boundary. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. Godefroy's Boundary Problem asks whether nevertheless both topologies have the same bounded compact sets. This paper contains the answer in the positive. Archive classification: math.FA Mathematics Subject Classification: 46B20 The source file(s), boundary.tex: 30948 bytes, is(are) stored in gzipped form as 0807.2810.gz with size 10kb. The corresponding postcript file has gzipped size 76kb. Submitted from: Hermann.Pfitzner at univ-orleans.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2810 or http://arXiv.org/abs/0807.2810 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2810 or in gzipped form by using subject line get 0807.2810 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Jul 23 13:09:32 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id B66D7D086E; Wed, 23 Jul 2008 13:09:32 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by T. P. Hyt\"onen, J. L. Torrea, and D. V. Yakubovich Message-Id: <20080723180932.B66D7D086E at fourier.math.okstate.edu> Date: Wed, 23 Jul 2008 13:09:32 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The Littlewood--Paley--Rubio de Francia property of a Banach space for the case of equal intervals" by T. P. Hyt\"onen, J. L. Torrea, and D. V. Yakubovich. Abstract: Let $X$ be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of $X$-valued functions holds true for all disjoint collections of subintervals of the set of integers of equal length and for all exponents $p$ greater or equal than 2 if and only if the space $X$ is a UMD space of type 2. The same criterion is obtained for the case of subintervals of the real line and Fourier integrals instead of Fourier series. Archive classification: math.FA Mathematics Subject Classification: 42Bxx; 46B20 Remarks: To appear in The Royal Society of Edinburgh Proc. A (Mathematics) The source file(s), lpr-equal_v6_arx.tex: 41797 bytes, is(are) stored in gzipped form as 0807.2981.gz with size 14kb. The corresponding postcript file has gzipped size 97kb. Submitted from: dmitry.yakubovich at uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.2981 or http://arXiv.org/abs/0807.2981 or by email in unzipped form by transmitting an empty message with subject line uget 0807.2981 or in gzipped form by using subject line get 0807.2981 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Jul 23 13:10:15 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2C445D086E; Wed, 23 Jul 2008 13:10:15 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Alexey I. Popov and Vladimir G. Troitsky Message-Id: <20080723181015.2C445D086E at fourier.math.okstate.edu> Date: Wed, 23 Jul 2008 13:10:15 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A version of Lomonosov's theorem for collections of positive operators" by Alexey I. Popov and Vladimir G. Troitsky. Abstract: It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zero x in X and f in X* such that f(Tx)=0 for all T in A. In the case of algebras of adjoint operators on a dual Banach space, V.Lomonosov extended this as follows: without having a compact operator in the algebra, |f(Tx)| is less than or equal to the essential norm of the pre-adjoint operator T_* for all T in A. In this paper, we prove a similar extension (in case of adjoint operators) of a result of R.Drnovsek. Namely, we prove that if C is a collection of positive adjoint operators on a Banach lattice X satisfying certain conditions, then there exist non-zero positive x in X and f in X* such that f(Tx) is less than or equal to the essential norm of T_* for all T in C. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B65; 47A15 The source file(s), lom-drnov.tex: 31715 bytes, is(are) stored in gzipped form as 0807.3327.gz with size 10kb. The corresponding postcript file has gzipped size 86kb. Submitted from: vtroitsky at math.ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.3327 or http://arXiv.org/abs/0807.3327 or by email in unzipped form by transmitting an empty message with subject line uget 0807.3327 or in gzipped form by using subject line get 0807.3327 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Aug 1 15:46:06 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id B9124D084F; Fri, 1 Aug 2008 15:46:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jesus Araujo and Luis Dubarbie Message-Id: <20080801204605.B9124D084F at fourier.math.okstate.edu> Date: Fri, 1 Aug 2008 15:46:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Biseparating maps between Lipschitz function spaces" by Jesus Araujo and Luis Dubarbie. Abstract: For complete metric spaces $X$ and $Y$, a description of linear biseparating maps between spaces of vector-valued Lipschitz functions defined on $X$ and $Y$ is provided. In particular it is proved that $X$ and $Y$ are bi-Lipschitz homeomorphic, and the automatic continuity of such maps is derived in some cases. Besides, these results are used to characterize the separating bijections between scalar-valued Lipschitz function spaces when $Y$ is compact. Archive classification: math.FA Mathematics Subject Classification: Primary 47B38; Secondary 46E40, 46H40, 47B33 Remarks: 17 pages; no figures The source file(s), lipschitz86.tex: 48992 bytes, is(are) stored in gzipped form as 0807.3835.gz with size 14kb. The corresponding postcript file has gzipped size 106kb. Submitted from: araujoj at unican.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.3835 or http://arXiv.org/abs/0807.3835 or by email in unzipped form by transmitting an empty message with subject line uget 0807.3835 or in gzipped form by using subject line get 0807.3835 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Aug 1 15:47:25 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 97B06D084F; Fri, 1 Aug 2008 15:47:23 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Daniel Carando, Veronica Dimant and Pablo Sevilla-Peris Message-Id: <20080801204724.97B06D084F at fourier.math.okstate.edu> Date: Fri, 1 Aug 2008 15:47:23 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Multilinear Holder-type inequalities on Lorentz sequence spaces" by Daniel Carando, Veronica Dimant and Pablo Sevilla-Peris. Abstract: We establish H\"older type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals. Archive classification: math.FA Mathematics Subject Classification: 46A46, 46B45 The source file(s), CarandoDimantSevilla.tex: 59626 bytes, is(are) stored in gzipped form as 0807.4392.gz with size 18kb. The corresponding postcript file has gzipped size 122kb. Submitted from: dcarando at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0807.4392 or http://arXiv.org/abs/0807.4392 or by email in unzipped form by transmitting an empty message with subject line uget 0807.4392 or in gzipped form by using subject line get 0807.4392 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Aug 13 13:45:41 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2CA84D06AE; Wed, 13 Aug 2008 13:45:40 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Pawel Mleczko Message-Id: <20080813184541.2CA84D06AE at fourier.math.okstate.edu> Date: Wed, 13 Aug 2008 13:45:40 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Compact multipliers on spaces of analytic functions" by Pawel Mleczko. Abstract: In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\infty\hookrightarrow X\hookrightarrow H_1$, necessary and sufficient conditions for compactness are presented. Moreover, the calculation of the Hausdorff measure of noncompactness for diagonal operators between Banach sequence lattices is applied to obtaining the characterization of compact multipliers in case the domain space $X$ satisfies $H_\infty\hookrightarrow X\hookrightarrow H_2$. Archive classification: math.FA math.CV Mathematics Subject Classification: 42B15, 42B30, 46E05, 7B10 The source file(s), comp-multi.tex: 26131 bytes, is(are) stored in gzipped form as 0808.1359.gz with size 9kb. The corresponding postcript file has gzipped size 82kb. Submitted from: pml at amu.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.1359 or http://arXiv.org/abs/0808.1359 or by email in unzipped form by transmitting an empty message with subject line uget 0808.1359 or in gzipped form by using subject line get 0808.1359 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Aug 13 13:46:35 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 02000D06AE; Wed, 13 Aug 2008 13:46:34 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Guido Gherardi and Alberto Marcone Message-Id: <20080813184635.02000D06AE at fourier.math.okstate.edu> Date: Wed, 13 Aug 2008 13:46:34 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "How much incomputable is the separable Hahn-Banach theorem?" by Guido Gherardi and Alberto Marcone. Abstract: We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak Konig's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibility for multi-valued functions, we obtain a computational counterpart of the subsystem of second order arithmetic WKL_0. We study analogies and differences between WKL_0 and the class of Sep-computable multi-valued functions. Extending work of Brattka, we show that a natural multi-valued function associated with the Hahn-Banach Extension Theorem is Sep-complete. Archive classification: math.LO math.FA Mathematics Subject Classification: 03F60 (Primary) 03B30, 46A22, 46S30 (Secondary) The source file(s), HahnBanach.tex: 106451 bytes, is(are) stored in gzipped form as 0808.1663.gz with size 32kb. The corresponding postcript file has gzipped size 149kb. Submitted from: alberto.marcone at dimi.uniud.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.1663 or http://arXiv.org/abs/0808.1663 or by email in unzipped form by transmitting an empty message with subject line uget 0808.1663 or in gzipped form by using subject line get 0808.1663 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Aug 29 09:30:25 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 711EAD0879; Fri, 29 Aug 2008 09:30:25 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Denis Potapov and Fyodor Sukochev Message-Id: <20080829143025.711EAD0879 at fourier.math.okstate.edu> Date: Fri, 29 Aug 2008 09:30:25 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The Haar system in the preduals of hyperfinite factors" by Denis Potapov and Fyodor Sukochev. Abstract: We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types~$\hbox{II}_1$, $\hbox{II}_\infty$, $\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative $L^p$-space). Archive classification: math.FA Remarks: 18 pages The source file(s), haar_III_lambda.tex: 68404 bytes, is(are) stored in gzipped form as 0808.2851.gz with size 20kb. The corresponding postcript file has gzipped size 97kb. Submitted from: denis.potapov at flinders.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.2851 or http://arXiv.org/abs/0808.2851 or by email in unzipped form by transmitting an empty message with subject line uget 0808.2851 or in gzipped form by using subject line get 0808.2851 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Aug 29 09:31:38 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DC947D0879; Fri, 29 Aug 2008 09:31:38 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jeff Cheeger and Bruce Kleiner Message-Id: <20080829143138.DC947D0879 at fourier.math.okstate.edu> Date: Fri, 29 Aug 2008 09:31:38 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property" by Jeff Cheeger and Bruce Kleiner. Abstract: We prove the differentiability of Lipschitz maps X---->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direction of tangent vectors to suitable rectifiable curves. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 46B22 (primary), 46G05 (secondary) The source file(s), pirnp.bbl: 3004 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.3249 or http://arXiv.org/abs/0808.3249 or by email in unzipped form by transmitting an empty message with subject line uget 0808.3249 or in gzipped form by using subject line get 0808.3249 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 16:56:32 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 67D1AD090A; Fri, 12 Sep 2008 16:56:32 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Yauhen Radyna and Anna Sidorik Message-Id: <20080912215632.67D1AD090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 16:56:32 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Fourier transform of function on locally compact Abelian groups taking values in Banach spaces" by Yauhen Radyna and Anna Sidorik. Abstract: We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded operator. If $G$ is an infinite group then Fourier transform $F: L_2(G,X)\to L_2(\widehat G,X)$ is a bounded operator if and only if Banach space $X$ is isomorphic to a Hilbert one. Archive classification: math.FA Mathematics Subject Classification: 46C15, 43A25 Remarks: 9 pages The source file(s), Radyna_YM_Sidorik_AG_eng.tex: 30387 bytes, is(are) stored in gzipped form as 0808.4009.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: yauhen.radyna at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.4009 or http://arXiv.org/abs/0808.4009 or by email in unzipped form by transmitting an empty message with subject line uget 0808.4009 or in gzipped form by using subject line get 0808.4009 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 16:58:05 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D1B45D090A; Fri, 12 Sep 2008 16:58:05 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Zoltan Kannai Message-Id: <20080912215805.D1B45D090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 16:58:05 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Uniform convergence for convexification of dominated pointwise convergent continuous functions" by Zoltan Kannai. Abstract: The Lebesgue dominated convergence theorem of the measure theory implies that the Riemann integral of a bounded sequence of continuous functions over the interval [ 0,1] pointwise converging to zero, also converges to zero. The validity of this result is independent of measure theory, on the other hand, this result together with only elementary functional analysis, can generate measure theory itself. The mentioned result was also known before the appearance of measure theory, but the original proof was very complicated. For this reason this result, when presented in teaching, is generally obtained based on measure theory. Later, Eberlein gave an elementary, but still relatively complicated proof, and there were other simpler proofs but burdened with complicated concepts, like measure theory. In this paper we give a short and elementary proof even for the following strenghened form of the mentioned result: a bounded sequence of continuous functions defined on a compact topological space K pointwise converging to zero, has a suitable convexification converging also uniformly to zero on $K,$ thus, e.g., the original sequence converges weakly to zero in C(K). This fact can also be used in the proof of the Krein-Smulian theorem. The usual proof beyond the simple tools of the functional analysis, uses heavy embedding theorems and the Riesz' representation theorem with the whole apparatus of measure theory. Our main result, however, reduces the cited proof to a form in which we need abstract tools only, namely the Hahn-Banach separation theorem and Alaoglu's theorem, without Riesz' representation or any statement of measure theory. Archive classification: math.FA The source file(s), pointwise.tex: 12973 bytes, is(are) stored in gzipped form as 0809.0393.gz with size 4kb. The corresponding postcript file has gzipped size 48kb. Submitted from: kannai at uni-corvinus.hu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.0393 or http://arXiv.org/abs/0809.0393 or by email in unzipped form by transmitting an empty message with subject line uget 0809.0393 or in gzipped form by using subject line get 0809.0393 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 16:58:53 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 55905D090A; Fri, 12 Sep 2008 16:58:53 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Fulvio Ricci and Joan Verdera Message-Id: <20080912215853.55905D090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 16:58:53 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Duality in spaces of finite linear combinations of atoms" by Fulvio Ricci and Joan Verdera. Abstract: In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0<p\leq 1$ on ${\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on $(p,\infty)$-atoms, $0<p < 1$, whose analogue for $p=1$ is known to be false. Let $0 < p <1$ and let $T$ be a linear operator defined on the space of finite linear combinations of $(p,\infty)$-atoms, $0<p < 1 $, which takes values in a Banach space $B$. If $T$ is uniformly bounded on $(p,\infty)$-atoms, then $T$ extends to a bounded operator from $H^p({\mathbb R}^n)$ into $B$. Archive classification: math.FA Mathematics Subject Classification: 42B30 Remarks: 15 pages The source file(s), atoms.tex: 40423 bytes, is(are) stored in gzipped form as 0809.1719.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: fricci at sns.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1719 or http://arXiv.org/abs/0809.1719 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1719 or in gzipped form by using subject line get 0809.1719 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 16:59:50 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F1DB4D090A; Fri, 12 Sep 2008 16:59:49 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Jarno Talponen Message-Id: <20080912215949.F1DB4D090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 16:59:49 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Special symmetries of Banach spaces isomorphic to Hilbert spaces" by Jarno Talponen. Abstract: In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space. Archive classification: math.FA Mathematics Subject Classification: 46C15; 46B04 The source file(s), SSNSb.tex: 30955 bytes, is(are) stored in gzipped form as 0809.1789.gz with size 9kb. The corresponding postcript file has gzipped size 74kb. Submitted from: talponen at cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1789 or http://arXiv.org/abs/0809.1789 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1789 or in gzipped form by using subject line get 0809.1789 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 17:00:35 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 30730D090A; Fri, 12 Sep 2008 17:00:35 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Ioannis Gasparis Message-Id: <20080912220035.30730D090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 17:00:35 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "New examples of $c_0$-saturated Banach spaces" by Ioannis Gasparis. Abstract: For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a $C(K)$ space for every countable and compact metric space $K$. Archive classification: math.FA Mathematics Subject Classification: 46B03 The source file(s), satur.tex: 82312 bytes, is(are) stored in gzipped form as 0809.1808.gz with size 22kb. The corresponding postcript file has gzipped size 143kb. Submitted from: ioagaspa at math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1808 or http://arXiv.org/abs/0809.1808 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1808 or in gzipped form by using subject line get 0809.1808 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 17:01:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E1250D090A; Fri, 12 Sep 2008 17:01:14 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Ioannis Gasparis Message-Id: <20080912220114.E1250D090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 17:01:14 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "New examples of $c_0$-saturated Banach spaces II" by Ioannis Gasparis. Abstract: For every Banach space $Z$ with a shrinking unconditional basis satisfying upper $p$-estimates for some $p > 1$, an isomorphically polyhedral Banach space is constructed having an unconditional basis and admitting a quotient isomorphic to $Z$. Archive classification: math.FA Mathematics Subject Classification: 46B03 The source file(s), satur2.tex: 36833 bytes, is(are) stored in gzipped form as 0809.1815.gz with size 11kb. The corresponding postcript file has gzipped size 93kb. Submitted from: ioagaspa at math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1815 or http://arXiv.org/abs/0809.1815 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1815 or in gzipped form by using subject line get 0809.1815 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Fri Sep 12 17:07:13 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E1D0AD090A; Fri, 12 Sep 2008 17:07:13 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Christoph Haberl and Franz E. Schuster Message-Id: <20080912220713.E1D0AD090A at fourier.math.okstate.edu> Date: Fri, 12 Sep 2008 17:07:13 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "General Lp affine isoperimetric inequalities" by Christoph Haberl and Franz E. Schuster. Abstract: Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality. Archive classification: math.DG math.FA Mathematics Subject Classification: 52A40; 52A39 The source file(s), Lpaffine.tex: 76896 bytes, is(are) stored in gzipped form as 0809.1995.gz with size 20kb. The corresponding postcript file has gzipped size 116kb. Submitted from: franz.schuster at tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1995 or http://arXiv.org/abs/0809.1995 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1995 or in gzipped form by using subject line get 0809.1995 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 22 13:26:53 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 326ABD091F; Mon, 22 Sep 2008 13:26:53 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Antonio Aviles, Vladimir Kadets, Miguel Martin, Javier Meri, and Varvara Shepelska Message-Id: <20080922182653.326ABD091F at fourier.math.okstate.edu> Date: Mon, 22 Sep 2008 13:26:53 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Slicely countably determined Banach spaces. Applications to the Daugavet and the alternative Daugavet equations" by Antonio Aviles, Vladimir Kadets, Miguel Martin, Javier Meri, and Varvara Shepelska. Abstract: We introduce the class of slicely countably determined Banach spaces which contains in particular all spaces with the RNP and all spaces without copies of $\ell_1$. We present many examples and several properties of this class. We give some applications to Banach spaces with the Daugavet and the alternative Daugavet properties, lush spaces and Banach spaces with numerical index $1$. In particular, we show that the dual of a real infinite-dimensional Banach with the alternative Daugavet property contains $\ell_1$ and that operators which do not fix copies of $\ell_1$ on a space with the alternative Daugavet property satisfy the alternative Daugavet equation. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20. Secondary 46B03, 46B04, 46B22, 47A12 The source file(s), AvilesKadetsMartinMeriShepelska.tex: 107489 bytes, is(are) stored in gzipped form as 0809.2723.gz with size 30kb. The corresponding postcript file has gzipped size 172kb. Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.2723 or http://arXiv.org/abs/0809.2723 or by email in unzipped form by transmitting an empty message with subject line uget 0809.2723 or in gzipped form by using subject line get 0809.2723 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 22 13:27:40 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 6BEC1D091F; Mon, 22 Sep 2008 13:27:40 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by S. R. Cowell and N. J. Kalton Message-Id: <20080922182740.6BEC1D091F at fourier.math.okstate.edu> Date: Mon, 22 Sep 2008 13:27:40 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Asymptotic unconditionality" by S. R. Cowell and N. J. Kalton. Abstract: We show that a separable real Banach space embeds almost isometrically in a space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to \infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^* \in X^*$, $(x_n^*)$ is a weak$^*$-null sequence and both limits exist. If $X$ is reflexive then $Y$ can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46B20 Remarks: 26 pages. Submitted for publication. This is a replacement The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.2294 or http://arXiv.org/abs/0809.2294 or by email in unzipped form by transmitting an empty message with subject line uget 0809.2294 or in gzipped form by using subject line get 0809.2294 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 22 13:28:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 762DCD091F; Mon, 22 Sep 2008 13:28:17 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Detelin Dosev Message-Id: <20080922182817.762DCD091F at fourier.math.okstate.edu> Date: Mon, 22 Sep 2008 13:28:17 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Commutators on $\ell_1$" by Detelin Dosev. Abstract: The main result is that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17) to obtain this result and use this generalization to obtain partial results about the commutators on spaces $\X$ which can be represented as $\displaystyle \X\simeq \left ( \bigoplus_{i=0}^{\infty} \X\right)_{p}$ for some $1\leq p<\infty$ or $p=0$. In particular, it is shown that every compact operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus\cdots\oplus\ell_{p_n}$ is given. We also show that strictly singular operators on $\linf$ are commutators. Archive classification: math.FA Mathematics Subject Classification: 47B47 Remarks: 17 pages. Submitted to the Journal of Functional Analysis The source file(s), Commutators_l1.tex: 58728 bytes, is(are) stored in gzipped form as 0809.3047.gz with size 16kb. The corresponding postcript file has gzipped size 110kb. Submitted from: ddosev at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3047 or http://arXiv.org/abs/0809.3047 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3047 or in gzipped form by using subject line get 0809.3047 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 22 13:29:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9D707D091F; Mon, 22 Sep 2008 13:29:14 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Tuomas Hytonen Message-Id: <20080922182914.9D707D091F at fourier.math.okstate.edu> Date: Mon, 22 Sep 2008 13:29:14 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The vector-valued non-homogeneous Tb theorem" by Tuomas Hytonen. Abstract: The paper gives a Banach space-valued extension of the ``\(Tb\) theorem'' of Nazarov, Treil and Volberg (2003) concerning the boundedness of singular integral operators with respect to a measure \(\mu\), which only satisfies an upper control on the size of balls. Under the same assumptions as in their result, such operators are shown to be bounded on the Bochner spaces \(L^p(\mu;X)\) of functions with values in \(X\) --- a Banach space with the unconditionality property of martingale differences (UMD) and a certain maximal function property, which holds for all typical examples of UMD spaces. The new proof deals directly with all \(p\in(1,\infty)\) and relies on delicate estimates for the non-homogenous ``Haar'' functions, as well as McConnell's (1989) decoupling inequality for tangent martingale differences. Archive classification: math.FA math.CA Mathematics Subject Classification: 42B20;42B25; 46B09; 46E40; 60G46 Remarks: 40 pages, submitted for publication The source file(s), nonhomog.tex: 143196 bytes, is(are) stored in gzipped form as 0809.3097.gz with size 39kb. The corresponding postcript file has gzipped size 209kb. Submitted from: tuomas.hytonen at helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3097 or http://arXiv.org/abs/0809.3097 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3097 or in gzipped form by using subject line get 0809.3097 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 29 12:25:07 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8324FD086A; Mon, 29 Sep 2008 12:25:07 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak Message-Id: <20080929172507.8324FD086A at fourier.math.okstate.edu> Date: Mon, 29 Sep 2008 12:25:07 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Banach spaces of bounded Szlenk index II" by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: For every $\alpha<\omega_1$ we establish the existence of a separable Banach space whose Szlenk index is $\omega^{\alpha\omega+1}$ and which is universal for all separable Banach spaces whose Szlenk-index does not exceed $\omega^{\alpha\omega}$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates. Archive classification: math.FA math.AG Mathematics Subject Classification: 46B20, 54H05 The source file(s), szlenkII_new.tex: 57543 bytes, is(are) stored in gzipped form as 0809.3626.gz with size 17kb. The corresponding postcript file has gzipped size 122kb. Submitted from: schlump at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3626 or http://arXiv.org/abs/0809.3626 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3626 or in gzipped form by using subject line get 0809.3626 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 29 12:25:55 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 03F72D086A; Mon, 29 Sep 2008 12:25:54 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Miguel Martin Message-Id: <20080929172555.03F72D086A at fourier.math.okstate.edu> Date: Mon, 29 Sep 2008 12:25:54 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The group of isometries of a Banach space and duality" by Miguel Martin. Abstract: We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples concerning numerical index, hermitian operators and dissipative operators are also shown. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B04. Secondary: 46B10, 46E15, 47A12 Remarks: To appear in J. Funct. Anal. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3644 or http://arXiv.org/abs/0809.3644 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3644 or in gzipped form by using subject line get 0809.3644 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 29 12:26:33 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 70FCED086A; Mon, 29 Sep 2008 12:26:33 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Geraldo Botelho and Daniel Pellegrino Message-Id: <20080929172633.70FCED086A at fourier.math.okstate.edu> Date: Mon, 29 Sep 2008 12:26:33 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Coincidences for multiple summing mappings" by Geraldo Botelho and Daniel Pellegrino. Abstract: In this note we prove new coincidence results for multiple summing mappings, related to the cotypes of the Banach spaces involved. Archive classification: math.FA Remarks: 3 pages, to appear in the resumes of the meeting ENAMA, Second The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4171 or http://arXiv.org/abs/0809.4171 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4171 or in gzipped form by using subject line get 0809.4171 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 29 12:27:13 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5DEB2D086A; Mon, 29 Sep 2008 12:27:13 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by George Androulakis and Antoine Flattot Message-Id: <20080929172713.5DEB2D086A at fourier.math.okstate.edu> Date: Mon, 29 Sep 2008 12:27:13 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$" by George Androulakis and Antoine Flattot. Abstract: The main result of this paper is the existence of a hyperinvariant subspace of weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$, ($1 \leq p \leq \infty$) when the weight $v$ is in the class of ``generalized polynomials'' and the composition map is a bijective ergodic transform satisfying a given discrepancy. The work is based on the construction of a functional calculus initiated by Wermer and generalized by Davie. Archive classification: math.FA Mathematics Subject Classification: 47A15 ; 47A10; 47A60 The source file(s), WCO.tex: 48622 bytes, is(are) stored in gzipped form as 0809.4429.gz with size 14kb. The corresponding postcript file has gzipped size 122kb. Submitted from: giorgis at math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4429 or http://arXiv.org/abs/0809.4429 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4429 or in gzipped form by using subject line get 0809.4429 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Sep 29 12:27:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5137FD086A; Mon, 29 Sep 2008 12:27:46 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda Message-Id: <20080929172746.5137FD086A at fourier.math.okstate.edu> Date: Mon, 29 Sep 2008 12:27:46 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On dominated polynomials between Banach spaces" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this paper, among other results, we prove a conjecture concerning coincidence theorems for dominated polynomials. We also obtain an abstract version of Pietsch Domination Theorem (PDT) which unifies and generalizes several different nonlinear approaches; our result recovers, as a particular case, the well-known PDT for dominated multilinear mappings. Archive classification: math.FA Mathematics Subject Classification: 46B15; 46G25 Remarks: 10 pages The source file(s), conjecture19agosto2008-arxiv.tex: 34210 bytes, is(are) stored in gzipped form as 0809.4496.gz with size 10kb. The corresponding postcript file has gzipped size 85kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4496 or http://arXiv.org/abs/0809.4496 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4496 or in gzipped form by using subject line get 0809.4496 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 7 13:46:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 7D8C7D06B2; Tue, 7 Oct 2008 13:46:17 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by George Androulakis, Nigel Kalton, and Adi Tcaciuc Message-Id: <20081007184617.7D8C7D06B2 at fourier.math.okstate.edu> Date: Tue, 7 Oct 2008 13:46:17 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On Banach spaces containing $l_p$ or $c_0$" by George Androulakis, Nigel Kalton, and Adi Tcaciuc. Abstract: We use the Gowers block Ramsey theorem to characterize Banach spaces containing isomorphs of $\ell_p$ (for some $1 \leq p < \infty$) or $c_0$. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B40; 46B03 The source file(s), ellpAndKalTca.tex: 22204 bytes, is(are) stored in gzipped form as 0810.0325.gz with size 7kb. The corresponding postcript file has gzipped size 72kb. Submitted from: giorgis at math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0325 or http://arXiv.org/abs/0810.0325 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0325 or in gzipped form by using subject line get 0810.0325 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 7 13:48:32 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 22CDFD06B2; Tue, 7 Oct 2008 13:48:32 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Hadi Haghshenas Message-Id: <20081007184832.22CDFD06B2 at fourier.math.okstate.edu> Date: Tue, 7 Oct 2008 13:48:32 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Differentiability of Banach spaces via constructible sets" by Hadi Haghshenas. Abstract: the main goal of this paper is to prove that any Banach space X , that every dual ball in X** is weak* separable, or every weak* closed convex subset in X**is weak* separable , or every norm-closed convex set in X* is constructible, admits an equivalent Frechet differentiable norm. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 5 pages The source file(s), DIFFERENTIABILITYOFBANACHSPACESVIACONSTRUCTIBLESETS.tex: 12164 bytes, is(are) stored in gzipped form as 0810.0586.gz with size 5kb. The corresponding postcript file has gzipped size 43kb. Submitted from: h_haghshenas60 at yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0586 or http://arXiv.org/abs/0810.0586 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0586 or in gzipped form by using subject line get 0810.0586 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 7 13:50:15 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D715CD06B2; Tue, 7 Oct 2008 13:50:15 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Assadi, Hadi Haghshenas, and Hosseini Guive Message-Id: <20081007185015.D715CD06B2 at fourier.math.okstate.edu> Date: Tue, 7 Oct 2008 13:50:15 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Convexity of Chebyshev sets through differentiability of distance function" by Assadi, Hadi Haghshenas, and Hosseini Guive. Abstract: The aim of this paper is to present some equivalent conditions that ensure the convexity of a Chebyshev set. To do so, we use Gateaux differentiability of the distance function Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 4 pages The source file(s), CONVEXITYOFCEBYSEVSETSTHROUGHDIFFERENTIABILITYOFDISTANCEFUNCTION.tex: 10884 bytes, is(are) stored in gzipped form as 0810.0587.gz with size 4kb. The corresponding postcript file has gzipped size 41kb. Submitted from: h_haghshenas60 at yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0587 or http://arXiv.org/abs/0810.0587 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0587 or in gzipped form by using subject line get 0810.0587 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:20:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 11E49D094B; Tue, 28 Oct 2008 17:20:45 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by A. Assadi,HADI Haghshenas and H. Hosseini Guive Message-Id: <20081028222046.11E49D094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:20:45 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A review on some geometric results of the Smulian's theorem on Frechet differentiability of norms" by A. Assadi,HADI Haghshenas and H. Hosseini Guive. Abstract: In this paper, we prove the Smulian s theorem on Frechet differentiability of norm,and present some of its geometric results concerning the Gateaux and Frechet differentiability of norm and properties of the allied space and its dual such as reflexivity and strict convexity. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 4 Pages The source file(s), AREVIEWONSOMEGEOMETRICRESULTSOFTHESMULIANSTHEOREMONFRECHETDIFFERENTIABILITYOFNORMS.tex: 10646 bytes, is(are) stored in gzipped form as 0810.0773.gz with size 4kb. The corresponding postcript file has gzipped size 42kb. Submitted from: h_haghshenas60 at yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0773 or http://arXiv.org/abs/0810.0773 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0773 or in gzipped form by using subject line get 0810.0773 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:21:32 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id EB432D094B; Tue, 28 Oct 2008 17:21:32 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Hadi Haghshenas Message-Id: <20081028222132.EB432D094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:21:32 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Convexity of Chebyshev sets in Hilbert spaces" by Hadi Haghshenas. Abstract: The aim of this paper is state of conditions that ensure the convexity of a Chebyshev sets in Hilbert spaces . Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 4 Pages The source file(s), CONVEXITYOFCEBYSEVSETSINHILBERTSPACES.tex: 8784 bytes, is(are) stored in gzipped form as 0810.0772.gz with size 3kb. The corresponding postcript file has gzipped size 36kb. Submitted from: h_haghshenas60 at yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0772 or http://arXiv.org/abs/0810.0772 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0772 or in gzipped form by using subject line get 0810.0772 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:22:17 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 18D75D094B; Tue, 28 Oct 2008 17:22:16 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Libor Vesely and Ludek Zajicek Message-Id: <20081028222217.18D75D094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:22:16 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On extensions of d.c. functions and convex functions" by Libor Vesely and Ludek Zajicek. Abstract: We show how our recent results on compositions of d.c. functions (and mappings) imply positive results on extensions of d.c. functions (and mappings). Examples answering two natural relevant questions are presented. Two further theorems, concerning extendability of continuous convex functions from a closed subspace of a normed linear space, complement recent results of J.Borwein, V.Montesinos and J.Vanderwerff. Archive classification: math.FA math.GM Mathematics Subject Classification: 52A41; 26B25; 46B99 Remarks: 16 pages The source file(s), RozsirDCfinal.tex: 48466 bytes, is(are) stored in gzipped form as 0810.1433.gz with size 15kb. The corresponding postcript file has gzipped size 110kb. Submitted from: Libor.Vesely at mat.unimi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.1433 or http://arXiv.org/abs/0810.1433 or by email in unzipped form by transmitting an empty message with subject line uget 0810.1433 or in gzipped form by using subject line get 0810.1433 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:22:55 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id C2AD1D094B; Tue, 28 Oct 2008 17:22:55 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Javier Guachalla H Message-Id: <20081028222255.C2AD1D094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:22:55 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "$L^1$ is complemented in $L^{\infty *}$" by Javier Guachalla H. Abstract: We show $L^1$ is complemented in the dual space $L^{\infty *}$ Archive classification: math.FA The source file(s), l1cmplm.TEX: 2401 bytes, is(are) stored in gzipped form as 0810.2354.gz with size 1kb. The corresponding postcript file has gzipped size 29kb. Submitted from: jguachallah at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.2354 or http://arXiv.org/abs/0810.2354 or by email in unzipped form by transmitting an empty message with subject line uget 0810.2354 or in gzipped form by using subject line get 0810.2354 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:24:16 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D6447D094B; Tue, 28 Oct 2008 17:24:16 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Siu-Ah Ng Message-Id: <20081028222416.D6447D094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:24:16 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Bidual as a weak nonstandard hull" by Siu-Ah Ng. Abstract: We construct the weak nonstandard hull of a normed linear space X from *X (the nonstandard extension of X) using the weak topology on X. The bidual (i.e. the second dual) X'' is shown to be isometrically isomorphic to the weak nonstandard hull of X. Examples and applications to C*-algebras are given, including a simple proof of the Sherman-Takeda Theorem. As a consequence, the weak nonstandard hull of a C*-algebra is always a von Neumann algebra. Moreover a natural representation of the Arens product is given. Archive classification: math.FA math.LO math.OA Mathematics Subject Classification: 46L05, 03H05, 26E3,5 46S20 Remarks: 14 pages The source file(s), bidual.tex: 38768 bytes, is(are) stored in gzipped form as 0810.3090.gz with size 11kb. The corresponding postcript file has gzipped size 87kb. Submitted from: ngs at ukzn.ac.za The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.3090 or http://arXiv.org/abs/0810.3090 or by email in unzipped form by transmitting an empty message with subject line uget 0810.3090 or in gzipped form by using subject line get 0810.3090 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Oct 28 17:25:31 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 3BD7ED094B; Tue, 28 Oct 2008 17:25:31 -0500 (CDT) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by R. Fry Message-Id: <20081028222531.3BD7ED094B at fourier.math.okstate.edu> Date: Tue, 28 Oct 2008 17:25:31 -0500 (CDT) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Corrigendum to Approximation by C^{p}-smooth, Lipschitz functions on Banach spaces" [J. Math. Anal. Appl., 315 (2006), 599-605]" by R. Fry. Abstract: In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banach space with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex subset of X, then any uniformly continuous function f: Y->R can be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if Z is any Banach space and f:X->Z is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only on X. Archive classification: math.FA Mathematics Subject Classification: 46B20 Citation: Journal of Mathematical Analysis and Applications, Volume 348, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.3881 or http://arXiv.org/abs/0810.3881 or by email in unzipped form by transmitting an empty message with subject line uget 0810.3881 or in gzipped form by using subject line get 0810.3881 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 08:51:33 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A406AD0500; Tue, 4 Nov 2008 08:51:33 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Dusan Repovs and Pavel V. Semenov Message-Id: <20081104145133.A406AD0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 08:51:33 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On continuous choice of retractions onto nonconvex subsets" by Dusan Repovs and Pavel V. Semenov. Abstract: For a Banach space $B$ and for a class $\A$ of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements $A \in \A$ can be chosen to depend continuously on $A$, whenever nonconvexity of each $A \in \A$ is less than $\f{1}{2}$. The key geometric argument is that the set of all uniform retractions onto an $\a-$paraconvex set (in the spirit of E. Michael) is $\frac{\a}{1-\a}-$paraconvex subset in the space of continuous mappings of $B$ into itself. For a Hilbert space $H$ the estimate $\frac{\a}{1-\a}$ can be improved to $\frac{\a (1+\a^{2})}{1-\a^{2}}$ and the constant $\f{1}{2}$ can be reduced to the root of the equation $\a+ \a^{2}+a^{3}=1$. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60; 54C65; 41A65; 54C55; 54C20 The source file(s), VerzijaZaArhiv.tex: 38914 bytes, is(are) stored in gzipped form as 0810.3895.gz with size 12kb. The corresponding postcript file has gzipped size 89kb. Submitted from: dusan.repovs at guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.3895 or http://arXiv.org/abs/0810.3895 or by email in unzipped form by transmitting an empty message with subject line uget 0810.3895 or in gzipped form by using subject line get 0810.3895 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 08:52:28 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F4060D0500; Tue, 4 Nov 2008 08:52:27 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by R. Fry Message-Id: <20081104145227.F4060D0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 08:52:27 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Approximation by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces" by R. Fry. Abstract: It is shown that on weakly compactly generated Banach spaces which admit a Lipschitz, C^{p} smooth bump function, one can uniformly approximate uniformly continuous, bounded, real-valued functions by Lipschitz, C^{p} smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler. Archive classification: math.FA Mathematics Subject Classification: 46B20 Citation: Journal of Functional Analysis, Volume 252, Issue 1, 1 November The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.3901 or http://arXiv.org/abs/0810.3901 or by email in unzipped form by transmitting an empty message with subject line uget 0810.3901 or in gzipped form by using subject line get 0810.3901 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 08:55:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 5EEFCD0500; Tue, 4 Nov 2008 08:55:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Michael Cwikel and Eliahu Levy Message-Id: <20081104145529.5EEFCD0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 08:55:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Estimates for covering numbers in Schauder's theorem about adjoints of compact operators" by Michael Cwikel and Eliahu Levy. Abstract: Let T:X --> Y be a bounded linear map between Banach spaces X and Y. Let S:Y' --> X' be its adjoint. Let B(X) and B(Y') be the closed unit balls of X and Y' respectively. We obtain apparently new estimates for the covering numbers of the set S(B(Y')). These are expressed in terms of the covering numbers of T(B(X)), or, more generally, in terms of the covering numbers of a "significant" subset of T(B(X)). The latter more general estimates are best possible. These estimates follow from our new quantitative version of an abstract compactness result which generalizes classical theorems of Arzela-Ascoli and of Schauder. Analogous estimates also hold for the covering numbers of T(B(X)), in terms of the covering numbers of S(B(Y')) or in terms of a suitable "significant" subset of S(B(Y')). Archive classification: math.FA Mathematics Subject Classification: Primary 46B06. Secondary 46B10, 46B50, 05B40, 52C17, 52C15. Remarks: 14 pages. At any given time our most recent version of this paper will be either at http://www.math.technion.ac.il/~mcwikel/compact/QuantitativeSchauder.pdf or http://arxiv.org/abs/0810.4240 The source file(s), 8QuantitativeSchauder.tex: 51761 bytes, is(are) stored in gzipped form as 0810.4240.gz with size 15kb. The corresponding postcript file has gzipped size 105kb. Submitted from: mcwikel at math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.4240 or http://arXiv.org/abs/0810.4240 or by email in unzipped form by transmitting an empty message with subject line uget 0810.4240 or in gzipped form by using subject line get 0810.4240 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 08:56:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E576ED0500; Tue, 4 Nov 2008 08:56:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Christian Rosendal Message-Id: <20081104145629.E576ED0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 08:56:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Infinite asymptotic games" by Christian Rosendal. Abstract: We study infinite asymptotic games in Banach spaces with an F.D.D. and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into $\ell_p$ sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. These results are related to questions of rapidity of subsequence extraction from normalised weakly null sequences. Archive classification: math.FA math.LO Mathematics Subject Classification: Primary: 46B03, Secondary 03E15 The source file(s), AsymptoticGames42.tex: 71838 bytes, is(are) stored in gzipped form as 0608616.gz with size 22kb. The corresponding postcript file has gzipped size 0kb. Submitted from: rosendal at math.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math/0608616 or http://arXiv.org/abs/math/0608616 or by email in unzipped form by transmitting an empty message with subject line uget math/0608616 or in gzipped form by using subject line get math/0608616 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 09:09:51 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 1BCE4D0500; Tue, 4 Nov 2008 09:09:51 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Gilles Pisier Message-Id: <20081104150951.1BCE4D0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 09:09:51 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Remarks on the non-commutative Khintchine inequalities for $0<p<2$" by Gilles Pisier. Abstract: We show that the validity of the non-commutative Khintchine inequality for some $q$ with $1<q<2$ implies its validity (with another constant) for all $1\le p<q$. We prove this for the inequality involving the Rademacher functions, but also for more general ``lacunary'' sequences, or even non-commutative analogues of the Rademacher functions. For instance, we may apply it to the ``$Z(2)$-sequences'' previously considered by Harcharras. The result appears to be new in that case. It implies that the space $\ell^n_1$ contains (as an operator space) a large subspace uniformly isomorphic (as an operator space) to $R_k+C_k$ with $k\sim n^{\frac12}$. This naturally raises several interesting questions concerning the best possible such $k$. Unfortunately we cannot settle the validity of the non-commutative Khintchine inequality for $0<p<1$ but we can prove several would be corollaries. For instance, given an infinite scalar matrix $[x_{ij}]$, we give a necessary and sufficient condition for $[\pm x_{ij}]$ to be in the Schatten class $S_p$ for almost all (independent) choices of signs $\pm 1$. We also characterize the bounded Schur multipliers from $S_2$ to $S_p$. The latter two characterizations extend to $0<p<1$ results already known for $1\le p\le2$. In addition, we observe that the hypercontractive inequalities, proved by Carlen and Lieb for the Fermionic case, remain valid for operator space valued functions, and hence the Kahane inequalities are valid in this setting. Archive classification: math.OA math.FA The source file(s), Remarks-Khintchine.Oct24.tex: 85759 bytes, is(are) stored in gzipped form as 0810.5705.gz with size 26kb. The corresponding postcript file has gzipped size 175kb. Submitted from: pisier at math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.5705 or http://arXiv.org/abs/0810.5705 or by email in unzipped form by transmitting an empty message with subject line uget 0810.5705 or in gzipped form by using subject line get 0810.5705 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 09:12:56 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F24FFD0500; Tue, 4 Nov 2008 09:12:55 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Gianluca Cassese Message-Id: <20081104151255.F24FFD0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 09:12:55 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Sure wins, separating probabilities and the representation of linear functionals" by Gianluca Cassese. Abstract: We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely additive expectations. A version of Riesz decomposition based on this property is obtained as well as a characterisation of positive functionals on the space of integrable functions Archive classification: math.FA math.PR Mathematics Subject Classification: 28A25, 28C05 The source file(s), JMAAR1.tex: 32542 bytes, is(are) stored in gzipped form as 0709.3411.gz with size 11kb. The corresponding postcript file has gzipped size 283kb. Submitted from: g.cassese at economia.unile.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0709.3411 or http://arXiv.org/abs/0709.3411 or by email in unzipped form by transmitting an empty message with subject line uget 0709.3411 or in gzipped form by using subject line get 0709.3411 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Nov 4 09:13:32 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id AA0F0D0500; Tue, 4 Nov 2008 09:13:32 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by R. Fry and L. Keener Message-Id: <20081104151332.AA0F0D0500 at fourier.math.okstate.edu> Date: Tue, 4 Nov 2008 09:13:32 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Approximation by Lipschitz, analytic maps on certain Banach spaces" by R. Fry and L. Keener. Abstract: We show that on separable Banach spaces admitting a separating polynomial, any uniformly continuous, bounded, real-valued function can be uniformly approximated by Lipschitz, analytic maps on bounded sets. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 19 pages The source file(s), FryKeenerv2.tex: 58919 bytes, is(are) stored in gzipped form as 0810.5600.gz with size 15kb. The corresponding postcript file has gzipped size 111kb. Submitted from: rfry at tru.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.5600 or http://arXiv.org/abs/0810.5600 or by email in unzipped form by transmitting an empty message with subject line uget 0810.5600 or in gzipped form by using subject line get 0810.5600 to: math at arXiv.org. From: "Tong, Simei" <TONGS at uwec.edu> To: "'banach at math.okstate.edu'" <banach at math.okstate.edu> Subject: [Banach] Position at University of Wisconsin-Eau Claire Date: Thu, 6 Nov 2008 14:03:22 -0600 Department of Mathematics University of Wisconsin-Eau Claire A probationary tenure-track faculty position is available in the Department of Mathematics at the rank of Assistant Professor beginning August 24, 2009. See http://www.uwec.edu/acadaff/jobs/faculty/MathF-537.htm for further details. _______________________________________________
From alspach at fourier.math.okstate.edu Mon Nov 10 13:33:30 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F163CD094F; Mon, 10 Nov 2008 13:33:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by G. Botelho, D. Diniz and D. Pellegrino Message-Id: <20081110193329.F163CD094F at fourier.math.okstate.edu> Date: Mon, 10 Nov 2008 13:33:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A note on lineability of sets of bounded non-absolutely summing operators" by G. Botelho, D. Diniz and D. Pellegrino. Abstract: In this note we sketch a method to prove that several sets of bounded non-absolutely p-summing operators are lineable. We partially solve a question posed by Puglisi and Seoane-Sepulveda on this subject. Archive classification: math.FA Mathematics Subject Classification: 47B10 Remarks: 4 pages The source file(s), lin5.tex: 10790 bytes, is(are) stored in gzipped form as 0811.0092.gz with size 4kb. The corresponding postcript file has gzipped size 52kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0092 or http://arXiv.org/abs/0811.0092 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0092 or in gzipped form by using subject line get 0811.0092 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Nov 10 13:34:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 3456CD094F; Mon, 10 Nov 2008 13:34:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Piotr Koszmider, Miguel Martin, and Javier Meri Message-Id: <20081110193429.3456CD094F at fourier.math.okstate.edu> Date: Mon, 10 Nov 2008 13:34:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Extremely non-complex C(K) spaces" by Piotr Koszmider, Miguel Martin, and Javier Meri . Abstract: We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e.\ spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the positive Question 4.11 of [Kadets, Martin, Meri, Norm equalities for operators, \emph{Indiana U.\ Math.\ J.} \textbf{56} (2007), 2385--2411]. More concretely, we show that this is the case of some $C(K)$ spaces with few operators constructed in [Koszmider, Banach spaces of continuous functions with few operators, \emph{Math.\ Ann.} \textbf{330} (2004), 151--183] and [Plebanek, A construction of a Banach space $C(K)$ with few operators, \emph{Topology Appl.} \textbf{143} (2004), 217--239]. We also construct compact spaces $K_1$ and $K_2$ such that $C(K_1)$ and $C(K_2)$ are extremely non-complex, $C(K_1)$ contains a complemented copy of $C(2^\omega)$ and $C(K_2)$ contains a (1-complemented) isometric copy of $\ell_\infty$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B20, 47A99 Remarks: to appear in J. Math. Anal. Appl The source file(s), JMAA-07-3370R1.tex: 65250 bytes, is(are) stored in gzipped form as 0811.0577.gz with size 20kb. The corresponding postcript file has gzipped size 135kb. Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0577 or http://arXiv.org/abs/0811.0577 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0577 or in gzipped form by using subject line get 0811.0577 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Nov 10 13:35:43 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id A1C1CD094F; Mon, 10 Nov 2008 13:35:43 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Vladimir Kadets, Miguel Martin, Javier Meri, and Rafael Paya Message-Id: <20081110193543.A1C1CD094F at fourier.math.okstate.edu> Date: Mon, 10 Nov 2008 13:35:43 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Convexity and smoothness of Banach spaces with numerical index one" by Vladimir Kadets, Miguel Martin, Javier Meri, and Rafael Paya . Abstract: We show that a Banach space with numerical index one cannot enjoy good convexity or smoothness properties unless it is one-dimensional. For instance, it has no WLUR points in its unit ball, its norm is not Frechet smooth and its dual norm is neither smooth nor strictly convex. Actually, these results also hold if the space has the (strictly weaker) alternative Daugavet property. We construct a (non-complete) strictly convex predual of an infinite-dimensional $L_1$ space (which satisfies a property called lushness which implies numerical index~$1$). On the other hand, we show that a lush real Banach space is neither strictly convex nor smooth, unless it is one-dimensional. In particular, if a subspace $X$ of the real space $C[0,1]$ is smooth or strictly convex, then $C[0,1]/X$ contains a copy of $C[0,1]$. Finally, we prove that the dual of any lush infinite-dimensional real space contains a copy of $\ell_1$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B04, 46B20, 47A12 Remarks: Illinois J. Math. (to appear) The source file(s), Kadets-Martin-Meri-Paya.tex: 61549 bytes, is(are) stored in gzipped form as 0811.0808.gz with size 19kb. The corresponding postcript file has gzipped size 120kb. Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.0808 or http://arXiv.org/abs/0811.0808 or by email in unzipped form by transmitting an empty message with subject line uget 0811.0808 or in gzipped form by using subject line get 0811.0808 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 19 13:13:58 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id BD068D099B; Wed, 19 Nov 2008 13:13:58 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Rishad Shahmurov Message-Id: <20081119191358.BD068D099B at fourier.math.okstate.edu> Date: Wed, 19 Nov 2008 13:13:58 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "General Hormander and Mikhlin conditions for multipliers of Besov spaces" by Rishad Shahmurov. Abstract: Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated. Archive classification: math.FA math.CA Mathematics Subject Classification: 34G10, 35J25, 35J70 Remarks: 16 The source file(s), FMTWeightedB.tex: 57462 bytes, is(are) stored in gzipped form as 0811.1350.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: shahmurov at hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1350 or http://arXiv.org/abs/0811.1350 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1350 or in gzipped form by using subject line get 0811.1350 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 19 13:14:46 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 0371FD099B; Wed, 19 Nov 2008 13:14:45 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Marisa Zymonopoulou Message-Id: <20081119191446.0371FD099B at fourier.math.okstate.edu> Date: Wed, 19 Nov 2008 13:14:45 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A note on the Busemann-Petty problem for bodies of certain invariance" by Marisa Zymonopoulou. Abstract: The Busemann-Petty problem asks whether origin symmetric convex bodies in $\R^n$ with smaller hyperplane sections necessarily have smaller volume. The answer is affirmative if $n\leq 3$ and negative if $n\geq 4.$ We consider a class of convex bodies that have a certain invariance property with respect to their ordered k-tuples of coordinates in $\R^{kn}$ and prove the corresponding problem. Archive classification: math.FA The source file(s), kn.tex: 32692 bytes, is(are) stored in gzipped form as 0811.1593.gz with size 10kb. The corresponding postcript file has gzipped size 82kb. Submitted from: marisa at cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1593 or http://arXiv.org/abs/0811.1593 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1593 or in gzipped form by using subject line get 0811.1593 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 19 13:22:03 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 60273D099B; Wed, 19 Nov 2008 13:22:03 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by M.I. Ostrovskii Message-Id: <20081119192203.60273D099B at fourier.math.okstate.edu> Date: Wed, 19 Nov 2008 13:22:03 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Sufficient enlargements of minimal volume for finite dimensional normed linear spaces" by M.I. Ostrovskii. Abstract: Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {\it sufficient enlargement} for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P:Y\to X$ such that $P(B_Y)\subset A$. The main results of the paper: {\bf (1)} Each minimal-volume sufficient enlargement is linearly equivalent to a zonotope spanned by multiples of columns of a totally unimodular matrix. {\bf (2)} If a finite dimensional normed linear space has a minimal-volume sufficient enlargement which is not a parallelepiped, then it contains a two-dimensional subspace whose unit ball is linearly equivalent to a regular hexagon. Archive classification: math.FA Mathematics Subject Classification: 46B07, 52A21 Citation: J. Funct. Anal. 255 (2008), no. 3, 589-619 The source file(s), ost.tex: 97543 bytes, is(are) stored in gzipped form as 0811.1763.gz with size 28kb. The corresponding postcript file has gzipped size 173kb. Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1763 or http://arXiv.org/abs/0811.1763 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1763 or in gzipped form by using subject line get 0811.1763 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 19 13:23:07 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 9E38BD099B; Wed, 19 Nov 2008 13:23:07 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by M.I. Ostrovskii Message-Id: <20081119192307.9E38BD099B at fourier.math.okstate.edu> Date: Wed, 19 Nov 2008 13:23:07 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Compositions of projections in Banach spaces and relations between approximation properties" by M.I. Ostrovskii. Abstract: A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $\pi$-property in terms of norms of compositions of projections is found. Archive classification: math.FA Mathematics Subject Classification: 46B07 Citation: Rocky Mountain Journal of Mathematics, 38 (2008), no. 4, 1253-1262 The source file(s), ostr.tex: 21966 bytes, is(are) stored in gzipped form as 0811.1763.gz with size 7kb. The corresponding postcript file has gzipped size 79kb. Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.1763 or http://arXiv.org/abs/0811.1763 or by email in unzipped form by transmitting an empty message with subject line uget 0811.1763 or in gzipped form by using subject line get 0811.1763 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 19 13:24:30 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id E497ED099B; Wed, 19 Nov 2008 13:24:30 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Oscar Blasco and Jan van Neerven Message-Id: <20081119192430.E497ED099B at fourier.math.okstate.edu> Date: Wed, 19 Nov 2008 13:24:30 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Spaces of operator-valued functions measurable with respect to the strong operator topology" by Oscar Blasco and Jan van Neerven. Abstract: Let $X$ and $Y$ be Banach spaces and $(\Omega,\Sigma,\mu)$ a finite measure space. In this note we introduce the space $L^p[\mu;L(X,Y)]$ consisting of all (equivalence classes of) functions $\Phi:\Omega \mapsto L(X,Y)$ such that $\omega \mapsto \Phi(\omega)x$ is strongly $\mu$-measurable for all $x\in X$ and $\omega \mapsto \Phi(\omega)f(\omega)$ belongs to $L^1(\mu;Y)$ for all $f\in L^{p'}(\mu;X)$, $1/p+1/p'=1$. We show that functions in $L^p[\mu;\L(X,Y)]$ define operator-valued measures with bounded $p$-variation and use these spaces to obtain an isometric characterization of the space of all $L(X,Y)$-valued multipliers acting boundedly from $L^p(\mu;X)$ into $L^q(\mu;Y)$, $1\le q< p<\infty$. Archive classification: math.FA Mathematics Subject Classification: 28B05, 46G10 Remarks: 12 pages The source file(s), Blasco_vanNeerven/BlascoVanNeerven.tex: 40452 bytes Blasco_vanNeerven/newsymbol.sty: 440 bytes Blasco_vanNeerven/srcltx.sty: 6955 bytes, is(are) stored in gzipped form as 0811.2284.tar.gz with size 14kb. The corresponding postcript file has gzipped size 97kb. Submitted from: J.M.A.M.vanNeerven at tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.2284 or http://arXiv.org/abs/0811.2284 or by email in unzipped form by transmitting an empty message with subject line uget 0811.2284 or in gzipped form by using subject line get 0811.2284 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 26 16:08:43 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DFEE5D094A; Wed, 26 Nov 2008 16:08:43 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by W. T. Gowers Message-Id: <20081126220843.DFEE5D094A at fourier.math.okstate.edu> Date: Wed, 26 Nov 2008 16:08:43 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Decompositions, approximate structure, transference, and the Hahn-Banach theorem" by W. T. Gowers. Abstract: This paper is partly a survey of certain kinds of results and proofs in additive combinatorics, and partly a discussion of how useful the finite-dimensional Hahn-Banach theorem can be. The most interesting single result is probably a simpler proof of a key step in the proof of the Green-Tao theorem, but several other applications of the method are given. A similarly simplified proof of the Green-Tao transference principle was obtained independently (and expressed in a rather different language) by Reingold, Trevisan, Tulsiani and Vadhan. Archive classification: math.CO math.FA Mathematics Subject Classification: 05D99 Remarks: 48 pages The source file(s), newtransfer6.tex: 157325 bytes, is(are) stored in gzipped form as 0811.3103.gz with size 46kb. The corresponding postcript file has gzipped size 191kb. Submitted from: wtg10 at dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.3103 or http://arXiv.org/abs/0811.3103 or by email in unzipped form by transmitting an empty message with subject line uget 0811.3103 or in gzipped form by using subject line get 0811.3103 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 26 16:10:04 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id F11C8D094A; Wed, 26 Nov 2008 16:10:03 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Tuomas Hytonen and Lutz Weis Message-Id: <20081126221003.F11C8D094A at fourier.math.okstate.edu> Date: Wed, 26 Nov 2008 16:10:03 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "The Banach space-valued BMO, Carleson's condition, and paraproducts" by Tuomas Hytonen and Lutz Weis. Abstract: We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition corresponds to the L^2 case in our theory. The result is applied to give a new proof for the L^p-boundedness of paraproducts with a BMO symbol. A novel feature of the argument is that all p are covered at once in a completely interpolation-free manner. This is achieved by using the L^1 Carleson norm, and indicates the usefulness of this notion. Our approach is chosen so that all these results extend in a natural way to the case of X-valued functions, where X is a Banach space with the UMD property. Archive classification: math.FA Mathematics Subject Classification: 42B35; 42B20; 42B25; 46E40 Remarks: 14 pages, submitted The source file(s), carleson.tex: 56068 bytes, is(are) stored in gzipped form as 0811.3333.gz with size 16kb. The corresponding postcript file has gzipped size 106kb. Submitted from: tuomas.hytonen at helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.3333 or http://arXiv.org/abs/0811.3333 or by email in unzipped form by transmitting an empty message with subject line uget 0811.3333 or in gzipped form by using subject line get 0811.3333 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 26 16:10:42 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 89B43D094A; Wed, 26 Nov 2008 16:10:42 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda Message-Id: <20081126221042.89B43D094A at fourier.math.okstate.edu> Date: Wed, 26 Nov 2008 16:10:42 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "A unified Pietsch domination theorem" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc. Archive classification: math.FA Remarks: 10 pages The source file(s), abstract-PDT-20nov.tex: 32852 bytes, is(are) stored in gzipped form as 0811.3518.gz with size 9kb. The corresponding postcript file has gzipped size 81kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.3518 or http://arXiv.org/abs/0811.3518 or by email in unzipped form by transmitting an empty message with subject line uget 0811.3518 or in gzipped form by using subject line get 0811.3518 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Wed Nov 26 16:11:34 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8FF02D094A; Wed, 26 Nov 2008 16:11:34 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Matthew Daws, Hung Le Pham, and Stuart White Message-Id: <20081126221134.8FF02D094A at fourier.math.okstate.edu> Date: Wed, 26 Nov 2008 16:11:34 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Preduals of semigroup algebras" by Matthew Daws, Hung Le Pham, and Stuart White. Abstract: For a locally compact group $G$, the measure convolution algebra $M(G)$ carries a natural coproduct. In previous work, we showed that the canonical predual $C_0(G)$ of $M(G)$ is the unique predual which makes both the product and the coproduct on $M(G)$ weak$^*$-continuous. Given a discrete semigroup $S$, the convolution algebra $\ell^1(S)$ also carries a coproduct. In this paper we examine preduals for $\ell^1(S)$ making both the product and the coproduct weak$^*$-continuous. Under certain conditions on $S$, we show that $\ell^1(S)$ has a unique such predual. Such $S$ include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on $\ell^1(S)$ when $S$ is either $\mathbb Z_+\times\mathbb Z$ or $(\mathbb N,\cdot)$. Archive classification: math.FA Mathematics Subject Classification: 43A20; 22A20 Remarks: 17 pages, LaTeX The source file(s), semigroups.tex: 50737 bytes, is(are) stored in gzipped form as 0811.3987.gz with size 15kb. The corresponding postcript file has gzipped size 114kb. Submitted from: matt.daws at cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.3987 or http://arXiv.org/abs/0811.3987 or by email in unzipped form by transmitting an empty message with subject line uget 0811.3987 or in gzipped form by using subject line get 0811.3987 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Thu Dec 4 13:52:29 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id B4DB5D09A4; Thu, 4 Dec 2008 13:52:29 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by R. J. Smith and S. Troyanski Message-Id: <20081204195229.B4DB5D09A4 at fourier.math.okstate.edu> Date: Thu, 4 Dec 2008 13:52:29 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Unconditional bases and strictly convex dual renormings" by R. J. Smith and S. Troyanski. Abstract: We present equivalent conditions for a space $X$ with an unconditional basis to admit an equivalent norm with a strictly convex dual norm. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46B26; 46B15 The source file(s), unc_basis_dual_sc.tex: 45412 bytes, is(are) stored in gzipped form as 0811.4685.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: smith at math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0811.4685 or http://arXiv.org/abs/0811.4685 or by email in unzipped form by transmitting an empty message with subject line uget 0811.4685 or in gzipped form by using subject line get 0811.4685 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Dec 16 16:10:43 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 8383ED044D; Tue, 16 Dec 2008 16:10:43 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Boris Rubin Message-Id: <20081216221043.8383ED044D at fourier.math.okstate.edu> Date: Tue, 16 Dec 2008 16:10:43 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Comparison of volumes of convex bodies in real, complex, and quaternionic spaces" by Boris Rubin. Abstract: The classical Busemann-Petty problem (1956) asks, whether origin-symmetric convex bodies in $\mathbb {R}^n$ with smaller hyperplane central sections necessarily have smaller volumes. It is known, that the answer is affirmative if $n\le 4$ and negative if $n>4$. The same question can be asked when volumes of hyperplane sections are replaced by more general comparison functions. We give unified exposition of this circle of problems in real, complex, and quaternionic $n$-dimensional spaces. All cases are treated simultaneously. In particular, we show that the Busemann-Petty problem in the quaternionic $n$-dimensional space has an affirmative answer if and only if $n =2$. The method relies on the properties of cosine transforms on the unit sphere. Possible generalizations for spaces over Clifford algebras are discussed. Archive classification: math.FA Mathematics Subject Classification: 44A12; 52A38 Remarks: 38 pages The source file(s), quaternion3.tex: 107627 bytes, is(are) stored in gzipped form as 0812.1300.gz with size 35kb. The corresponding postcript file has gzipped size 182kb. Submitted from: borisr at math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.1300 or http://arXiv.org/abs/0812.1300 or by email in unzipped form by transmitting an empty message with subject line uget 0812.1300 or in gzipped form by using subject line get 0812.1300 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Dec 16 16:11:22 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 0440ED044D; Tue, 16 Dec 2008 16:11:21 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda Message-Id: <20081216221122.0440ED044D at fourier.math.okstate.edu> Date: Tue, 16 Dec 2008 16:11:21 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Factorization theorems for dominated polynomials" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However, this alternative scheme is shown not to be satisfactory until the equivalence is proved. Archive classification: math.FA Mathematics Subject Classification: 46G25 The source file(s), II-Factorization2dic08.tex: 15703 bytes, is(are) stored in gzipped form as 0812.1401.gz with size 5kb. The corresponding postcript file has gzipped size 62kb. Submitted from: dmpellegrino at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.1401 or http://arXiv.org/abs/0812.1401 or by email in unzipped form by transmitting an empty message with subject line uget 0812.1401 or in gzipped form by using subject line get 0812.1401 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Dec 16 16:12:14 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 2D892D044D; Tue, 16 Dec 2008 16:12:14 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Robin Nittka Message-Id: <20081216221214.2D892D044D at fourier.math.okstate.edu> Date: Tue, 16 Dec 2008 16:12:14 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "On a new type concept for Banach spaces" by Robin Nittka. Abstract: In order to measure qualitative properties we introduce a new notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. As an application we give a new proof that certain classical Banach spaces are non-isomorphic. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 7 pages The source file(s), type.bbl: 1571 bytes type.tex: 27062 bytes, is(are) stored in gzipped form as 0812.2216.tar.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. Submitted from: robin.nittka at uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2216 or http://arXiv.org/abs/0812.2216 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2216 or in gzipped form by using subject line get 0812.2216 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Tue Dec 16 16:12:45 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id DE7B9D044D; Tue, 16 Dec 2008 16:12:45 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Roman Vershynin Message-Id: <20081216221245.DE7B9D044D at fourier.math.okstate.edu> Date: Tue, 16 Dec 2008 16:12:45 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Spectral norm of products of random and deterministic matrices" by Roman Vershynin. Abstract: We study the spectral norm of matrices M that can be factored as M=BA, where A is a random matrix with independent mean zero entries, and B is a fixed matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show that the spectral norm of such an m by n matrix M is bounded by \sqrt{m} + \sqrt{n}, which is sharp. In other words, in regard to the spectral norm, products of random and deterministic matrices behave similarly to random matrices with independent entries. This result along with the previous work of M. Rudelson and the author implies that the smallest singular value of a random m times n matrix with i.i.d. mean zero entries and bounded (4+epsilon)-th moment is bounded below by \sqrt{m} - \sqrt{n-1} with high probability. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52; 46B09 Remarks: 34 pages, no figures The source file(s), product-random-deterministic.tex: 81516 bytes, is(are) stored in gzipped form as 0812.2432.gz with size 22kb. The corresponding postcript file has gzipped size 147kb. Submitted from: romanv at umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2432 or http://arXiv.org/abs/0812.2432 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2432 or in gzipped form by using subject line get 0812.2432 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Dec 29 12:01:11 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id 93B0FD044D; Mon, 29 Dec 2008 12:01:11 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Kenneth R. Davidson and Alex Wright Message-Id: <20081229180111.93B0FD044D at fourier.math.okstate.edu> Date: Mon, 29 Dec 2008 12:01:11 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Operator algebras with unique preduals" by Kenneth R. Davidson and Alex Wright. Abstract: We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak*-closed unital operator operator algebra containing a weak* dense subalgebra of compact operators has a unique Banach space predual. Archive classification: math.OA math.FA Mathematics Subject Classification: 47L50; 46B04; 47L35 Remarks: 13 pages The source file(s), DavidsonWright3a.tex: 44578 bytes, is(are) stored in gzipped form as 0812.3159.gz with size 14kb. The corresponding postcript file has gzipped size 96kb. Submitted from: krdavids at uwaterloo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.3159 or http://arXiv.org/abs/0812.3159 or by email in unzipped form by transmitting an empty message with subject line uget 0812.3159 or in gzipped form by using subject line get 0812.3159 to: math at arXiv.org.
From alspach at fourier.math.okstate.edu Mon Dec 29 12:01:56 2008 Return-Path: <alspach at fourier.math.okstate.edu> X-Original-To: alspach Delivered-To: alspach at fourier.math.okstate.edu Received: by fourier.math.okstate.edu (Postfix, from userid 1005) id D1742D044D; Mon, 29 Dec 2008 12:01:56 -0600 (CST) To: alspach at fourier.math.okstate.edu, banach at mail.math.okstate.edu Subject: Abstract of a paper by Elisabeth Werner and Deping Ye Message-Id: <20081229180156.D1742D044D at fourier.math.okstate.edu> Date: Mon, 29 Dec 2008 12:01:56 -0600 (CST) From: alspach at fourier.math.okstate.edu (Dale Alspach) Status: R
This is an announcement for the paper "Inequalities for mixed $p$-affine surface area" by Elisabeth Werner and Deping Ye. Abstract: We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of $L_p$ affine surface areas, mixed $p$-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Remarks: 39 pages The source file(s), MixedLp.tex: 97032 bytes, is(are) stored in gzipped form as 0812.4550.gz with size 26kb. The corresponding postcript file has gzipped size 162kb. Submitted from: elisabeth.werner at case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.4550 or http://arXiv.org/abs/0812.4550 or by email in unzipped form by transmitting an empty message with subject line uget 0812.4550 or in gzipped form by using subject line get 0812.4550 to: math at arXiv.org.