Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikhail Ostrovskii From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:10:12 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Metric characterizations of superreflexivity in terms of word groups and finite graphs" by Mikhail Ostrovskii. Abstract: We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups. We compare characterizations of superreflexivity in terms of diamond graphs and binary trees. We show that there exist sequences of series-parallel graphs of increasing topological complexity which admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superreflexivity. Archive classification: math.MG math.CO math.FA math.GR Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12, 20F67, 46B07 Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4627 or http://arXiv.org/abs/1312.4627

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Diana Ojeda-Aristizabal From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:12:15 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Finite forms of Gowers' theorem on the oscillation stability of $c_0$" by Diana Ojeda-Aristizabal. Abstract: We give a constructive proof of the finite version of Gowers' $FIN_k$ Theorem and analyse the corresponding upper bounds. The $FIN_k$ Theorem is closely related to the oscillation stability of $c_0$. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was studied well before by V. Milman. We compare the finite $FIN_k$ Theorem with the finite stabilization principle in the case of spaces of the form $\ell_{\infty}^n$, $n\in\mathbb{N}$ and establish a much slower growing upper bound for the finite stabilization principle in this particular case. Archive classification: math.CO math.FA Mathematics Subject Classification: 05D10 Remarks: 18 pages Submitted from: dco34 at cornell.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4639 or http://arXiv.org/abs/1312.4639

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mohammad N. Ivaki From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:14:19 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The planar Busemann-Petty centroid inequality and its stability" by Mohammad N. Ivaki. Abstract: In [Centro-affine invariants for smooth convex bodies, Int. Math. Res. Notices. doi: 10.1093/imrn/rnr110, 2011] Stancu introduced a family of centro-affine normal flows, $p$-flow, for $1\leq p<\infty.$ Here we investigate the asymptotic behavior of the planar $p$-flow for $p=\infty$, in the class of smooth, origin-symmetric convex bodies. The motivation is the Busemann-Petty centroid inequality. First, we prove that the $\infty$-flow evolves appropriately normalized origin-symmetric solutions to the unit disk in the Hausdorff metric, modulo $SL(2).$ Second, as an application of this weak convergence, we prove the planar Busemann-Petty centroid inequality in the of class convex bodies having the origin of the plane in their interiors. Third, using the $\infty$-flow, we prove a stability version of the planar Busemann-Petty centroid inequality, in the Banach-Mazur distance, in the class of origin-symmetric convex bodies. Fourth, we prove that the convergence in the Hausdorff metric can be improved to convergence in the $\mathcal{C}^{\infty}$ topology. Archive classification: math.DG math.FA Mathematics Subject Classification: Primary 52A40, 53C44, 52A10, Secondary 35K55, 53A15 Remarks: Two preprints unified into one Submitted from: mohammad.ivaki at tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.4834 or http://arXiv.org/abs/1312.4834

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikhail Ostrovskii From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:16:10 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Metric spaces nonembeddable into Banach spaces with the property and thick families of geodesics" by Mikhail Ostrovskii. Abstract: We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that any thick family of geodesics is not Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikod\'ym property contains a bilipschitz image of a thick family of geodesics. Archive classification: math.MG math.FA Mathematics Subject Classification: Primary 30L05, Secondary: 46B22, 46B85 Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.5381 or http://arXiv.org/abs/1312.5381

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Alexander Koldobsky From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:19:07 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A hyperplane inequality for measures of unconditional convex bodies" by Alexander Koldobsky. Abstract: We prove an inequality that extends to arbitrary measures the hyperplane inequality for volume of unconditional convex bodies originally observed by Bourgain. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20 Submitted from: koldobskiya at missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.7048 or http://arXiv.org/abs/1312.7048

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sun Kwang Kim, Han Ju Lee and Miguel Martin From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:21:06 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On the Bishop-Phelps-Bollobas property for numerical radius" by Sun Kwang Kim, Han Ju Lee and Miguel Martin. Abstract: We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-$\nuu$) and find sufficient conditions for Banach spaces ensuring the BPBp-$\nuu$. Among other results, we show that $L_1(\mu)$-spaces have this property for every measure $\mu$. On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-$\nuu$. In particular, this shows that the Radon-Nikod\'{y}m property (even reflexivity) is not enough to get BPBp-$\nuu$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: hanjulee at dongguk.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.7698 or http://arXiv.org/abs/1312.7698

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Fresen From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:23:24 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Explicit Euclidean embeddings in permutation invariant normed spaces" by Daniel Fresen. Abstract: Let $(X,\left\Vert \cdot \right\Vert )$ be a real normed space of dimension $N\in \mathbb{N}$ with a basis $(e_{i})_{1}^{N}$ such that the norm is invariant under coordinate permutations. Assume for simplicity that the basis constant is at most $2$. Consider any $n\in \mathbb{N}$ and $0<\varepsilon <1/4$ such that $n\leq c(\log \varepsilon ^{-1})^{-1}\log N$. We provide an explicit construction of a matrix that generates a $(1+\varepsilon )$ embedding of $\ell _{2}^{n}$ into $X$. Archive classification: math.FA Mathematics Subject Classification: 46B06, 46B07, 52A20, 52A21, 52A23 Remarks: 14 pages Submitted from: daniel.fresen at yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0203 or http://arXiv.org/abs/1401.0203

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by D. Carando, S. Lassalle, and M. Mazzitelli From: alspach at math.okstate.edu (Dale Alspach) Date: Sat, 4 Jan 2014 15:25:44 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A Lindenstrauss theorem for some classes of multilinear mappings" by D. Carando, S. Lassalle, and M. Mazzitelli. Abstract: Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their norms. We also consider the class of symmetric multilinear mappings. Archive classification: math.FA Remarks: 11 pages Submitted from: mmazzite at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0488 or http://arXiv.org/abs/1401.0488

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski From: Jose Rodriguez <joserr at um.es> Date: Wed, 15 Jan 2014 11:44:57 +0100 To: banach at math.okstate.edu

Dear colleagues: This is the second announcement of the conference Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski which will be held in Albacete (Spain) on June 10-13, 2014, on the occasion of the 70th birthday of Professor Troyanski. Our web page at https://sites.google.com/site/geometryofbanachspaces/ contains detailed information about the conference. Main speakers who accepted our invitation are: S. Argyros, J. Castillo, S. Dilworth, M. Fabian, V. Fonf, G. Godefroy, P. Hajek, R. Haydon, F. Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, T. Schlumprecht, R. Smith, A. Suarez Granero. Registration is OPEN. Participants must pay a fee which will cover conference materials, lunches and coffee breaks during the conference. Details about the payment can be found in our web page. - Deadline for early registration: April 30. - Deadline for late registration: May 31. Participants will have the opportunity to deliver a short talk. The deadline for abstract submission is May 15. Accommodation: the conference web page includes a list of hotels in Albacete offering special rates for the participants. Please do not hesitate in contacting us at geometry.banach.spaces.2014 at gmail.com if you need further information. Looking forward to meeting you! The organizers, A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Fernando Albiac and Jose L. Ansorena From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:36:03 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Non-existence of greedy bases in direct sums of mixed $\ell_{p}$ spaces" by Fernando Albiac and Jose L. Ansorena. Abstract: The fact that finite direct sums of two or more mutually different spaces from the family $\{\ell_{p} : 1\le p<\infty\}\cup c_{0}$ fail to have greedy bases is stated in [Dilworth et al., Greedy bases for Besov spaces, Constr. Approx. 34 (2011), no. 2, 281-296]. However, the concise proof that the authors give of this fundamental result in greedy approximation relies on a fallacious argument, namely the alleged uniqueness of unconditional basis up to permutation of the spaces involved. The main goal of this note is to settle the problem by providing a correct proof. For that we first show that all greedy bases in an $\ell_{p}$ space have fundamental functions of the same order. As a by-product of our work we obtain that {\it every} almost greedy basis of a Banach space with unconditional basis and nontrivial type contains a greedy subbasis. Archive classification: math.FA Mathematics Subject Classification: 41A35, 46B15 46B45, 46T99 Submitted from: joseluis.ansorena at unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.0693 or http://arXiv.org/abs/1401.0693

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Wilson Cuellar-Carrera From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:37:55 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A Banach space with a countable infinite number of complex structures" by Wilson Cuellar-Carrera. Abstract: We give examples of real Banach spaces with exactly infinite countably many complex structures and with $\omega_1$ many complex structures. Archive classification: math.FA Submitted from: cuellar at ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.1781 or http://arXiv.org/abs/1401.1781

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Dale E. Alspach and Eloi Medina Galego From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:40:36 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A complete classification of the spaces of compact operators on C([1,alpha], l_p) spaces, 1<p< infinity" by Dale E. Alspach and Eloi Medina Galego. Abstract: We complete the classification, up to isomorphism, of the spaces of compact operators on C([1, gamma], l_p) spaces, 1<p< infinity. In order to do this, we classify, up to isomorphism, the spaces of compact operators {\mathcal K}(E, F), where E= C([1, lambda], l_p) and F=C([1,xi], l_q) for arbitrary ordinals lambda and xi and 1< p \leq q< infinity. More precisely, we prove that it is relatively consistent with ZFC that for any infinite ordinals lambda, mu, xi and eta the following statements are equivalent: (a) {\mathcal K}(C([1, lambda], l_p), C([1, xi], l_q)) is isomorphic to {\mathcal K}(C([1, mu], l_p), C([1, eta], l_q)) . (b) lambda and mu have the same cardinality and C([1,xi]) is isomorphic to C([1, eta]) or there exists an uncountable regular ordinal alpha and 1 \leq m, n < omega such that C([1, xi]) is isomorphic to C([1, alpha m]) and C([1,eta]) is isomorphic to C([1, alpha n]). Moreover, in ZFC, if lambda and mu are finite ordinals and xi and eta are infinite ordinals then the statements (a) and (b') are equivalent. (b') C([1,xi]) is isomorphic to C([1, eta]) or there exists an uncountable regular ordinal alpha and 1 \leq m, n \leq omega such that C([1, xi]) is isomorphic to C([1, alpha m]) and C([1,eta]) is isomorphic to C([1, alpha n]). Archive classification: math.FA Mathematics Subject Classification: 46B03 (primary) 46B25 (secondary) Remarks: Revised version will appear in Proc. AMS Submitted from: alspach at math.okstate.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.1857 or http://arXiv.org/abs/1401.1857

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Andrzej Wisnicki From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:42:22 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Hyper-extensions in metric fixed point theory" by Andrzej Wisnicki. Abstract: We apply a modern axiomatic system of nonstandard analysis in metric fixed point theory. In particular, we formulate a nonstandard iteration scheme for nonexpansive mappings and present a nonstandard approach to fixed-point problems in direct sums of Banach spaces. Archive classification: math.FA math.LO Remarks: 12 pages Submitted from: awisnic at hektor.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.2144 or http://arXiv.org/abs/1401.2144

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Dusan Repovs and Pavel V. Semenov From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:44:30 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Continuous selections of multivalued mappings" by Dusan Repovs and Pavel V. Semenov. Abstract: This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume. Archive classification: math.GN math.FA math.GT math.OC Mathematics Subject Classification: 54C60, 54C65, 28B20, 26E25, 49J53, 58C06 Citation: Recent Progress in General Topology III, (K. P. Hart, Jan van The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.2257 or http://arXiv.org/abs/1401.2257

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Tim de Laat and Mikael de la Salle From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:45:55 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Strong property (T) for higher rank simple Lie groups" by Tim de Laat and Mikael de la Salle. Abstract: We prove that connected higher rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces $\mathcal{E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as well. This generalizes the result of Lafforgue asserting that $\mathrm{SL}(3,\mathbb{R})$ has strong property (T) with respect to Hilbert spaces and the more recent result of the second named author asserting that $\mathrm{SL}(3,\mathbb{R})$ has strong property (T) with respect to a certain larger class of Banach spaces. For the generalization to higher rank groups, it is sufficient to prove strong property (T) for $\mathrm{Sp}(2,\mathbb{R})$ and its universal covering group. As consequences of our main result, it follows that for $X \in \mathcal{E}_{10}$, connected higher rank simple Lie groups and their lattices have property (F$_X$) of Bader, Furman, Gelander and Monod, and the expanders contructed from a lattice in such a group do not admit a coarse embedding into $X$. Archive classification: math.GR math.FA math.MG Report Number: CPH-SYM-DNRF92 Remarks: 30 pages, 1 figure Submitted from: tim.delaat at wis.kuleuven.be The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.3611 or http://arXiv.org/abs/1401.3611

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Rainis Haller and Johann Langemets From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:47:38 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Geometry of Banach spaces with an octahedral norm" by Rainis Haller and Johann Langemets. Abstract: We discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering of the unit ball. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Submitted from: johann.langemets at ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.3612 or http://arXiv.org/abs/1401.3612

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Ian Doust, Stephen Sanchez and Anthony Weston From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 17 Jan 2014 14:50:22 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The generalized roundness of $\ell_\infty^{(3)}$ revisited" by Ian Doust, Stephen Sanchez and Anthony Weston. Abstract: Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p \leq 2$. Lennard, Tonge and Weston gave an indirect proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero by appealing to highly non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this paper we give a direct proof that $\ell_{\infty}^{(3)}$ has generalized roundness zero. This provides insight into the combinatorial geometry of $\ell_{\infty}^{(3)}$ that causes the generalized roundness inequalities to fail. We complete the paper by noting a characterization of real quasi-normed spaces of generalized roundness zero. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 8 pages 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/1401.4095 or http://arXiv.org/abs/1401.4095

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Universality Meeting, Kent State University, April 11-13, 2014 From: Dale Alspach <alspach at math.okstate.edu> Date: Thu, 23 Jan 2014 14:54:16 -0600 To: banach at math.okstate.edu

Announcing an Informal Analysis Seminar focusing on Universality Friday afternoon, April 11, 2014 through early Sunday afternoon, April 13, 2014 This meeting has received generous funding from Elsevier, with additional support from Kent State University. This meeting should be especially attractive to non-specialists, and in particular to students and new PhD's. The reason is that the Friday afternoon session is being devoted to three expository talks, aimed at a non- specialist audience, on Universality by three excellent speakers: Paul Gauthier (Montreal), Pamela Gorkin (Bucknell), and Vassili Nestoridis (Athens). Our speakers on Saturday and Sunday will be Juan Bès, Kit Chan, Paul Gauthier, Pamela Gorkin, Manuel Maestre, Myrto Manolaki, Vassili Nestoridis, and Rebecca Sanders. Also, there is a reasonable possibility of (very) partial support for students and junior participants. Registration is free, but we ask intending participants to let us know of their interest. For further information, please consult: http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/April_2014.html and/or contact Richard Aron at aron at math.kent.edu . -------------- next part -------------- A non-text attachment was scrubbed... Name: kent_st_announcement.pdf Type: application/pdf Size: 46844 bytes Desc: not available URL: <http://cauchy.math.okstate.edu/pipermail/banach/attachments/20140123/2264d9c2/attachment.pdf> _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Integration, Vector Measures and Related Topics VI From: Grzegorz Plebanek <gplebanek at gmail.com> Date: Fri, 24 Jan 2014 18:08:30 +0100 To: banach at math.okstate.edu

2nd announcement on the conference *** Integration, Vector Measures and Related Topics VI *** June 15 - 21, 2014 *** the Mathematical Research and Conference Center in Bedlewo (near Poznan, Poland), Registration and more information on the conference webpage: http://www.math.uni.wroc.pl/~drygier/ivmrt2014/ Invited speakers: Antonio Aviles (Murcia), Erik J. Balder (Utrecht), Oscar Blasco (Valencia) Guillermo Curbera (Sevilla), Luisa Di Piazza (Palermo), Harold Garth Dales (Lancaster) Joe Diestel (Kent), Christian Hess (Paris), Marian Fabian (Prague), David H. Fremlin (Colchester) Ondrej Kalenda (Prague), Zbigniew Lipecki (Wrocław), Jose Rodriguez (Murcia) The organizing committee: M. Balcerzak, M. Cichon, K. Musial, G. Plebanek _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Conference Announcement Date: Sat, 25 Jan 2014 11:17:50 CST To: banach at math.okstate.edu From: Krzysztof Jarosz <krzysztof.m.jarosz at gmail.com>

7th Conference on Function Spaces will take place at the SIUE campus between Ma y 20 and May 24, 2014: http://www.siue.edu/MATH/conference2014/ We received an NSF grant to defer travel and local cost primarily for the parti cipants without other sources of funding. Krzysztof Jarosz Department of Mathematics and Statistics Southern Illinois University Edwardsville Edwardsville, IL 62026-1653, USA tel.: (618) 650-2354 fax: (618) 650-3771 e-mail: kjarosz at siue.edu http://www.siue.edu/~kjarosz/ _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Timur Oikhberg and Eugeniu Spinu From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:12:44 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Subprojective Banach spaces" by Timur Oikhberg and Eugeniu Spinu. Abstract: A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces. Archive classification: math.FA Submitted from: spinu at ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.4231 or http://arXiv.org/abs/1401.4231

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Cesar Ruiz and Victor M. Sanchez From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:14:38 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Nonlinear subsets of functions spaces and spaceability" by Cesar Ruiz and Victor M. Sanchez. Abstract: In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the same problem is studied for Nakano spaces assuming different hypothesis. Archive classification: math.FA Mathematics Subject Classification: 46E30 Remarks: 11 pages Submitted from: victorms at mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.5906 or http://arXiv.org/abs/1401.5906

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Pierre Youssef From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:16:35 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Extractig a basis with fixed block inside a matrix" by Pierre Youssef. Abstract: Given $U$ an $n\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a "good" block $V$. Archive classification: math.FA Submitted from: pierre.youssef at univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.6434 or http://arXiv.org/abs/1401.6434

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Maria Roginskaya and Michal Wojciechowski From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:18:25 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Bounded Approximation Property for Sobolev spaces on simply-connected planar domains" by Maria Roginskaya and Michal Wojciechowski. Abstract: We show that Sobolev space $W^1_1(\Omega)$ of any planar one-connected domain $\Omega$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $\Omega$. The prove is based on a new decomposition of a planar domain. Archive classification: math.FA Submitted from: maria.roginskaya at chalmers.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7131 or http://arXiv.org/abs/1401.7131

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Umut Caglar and Elisabeth M. Werner From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:19:56 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Mixed f-divergence and inequalities for log concave functions" by Umut Caglar and Elisabeth M. Werner. Abstract: Mixed f-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions. Special cases of f-divergences are mixed L_\lambda-affine surface areas for log concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santalo type inequality. Archive classification: math.FA 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/1401.7065 or http://arXiv.org/abs/1401.7065

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Domenico Candeloro and Anna Rita Sambucini From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:22:43 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Filter convergence and decompositions for vector lattice-valued" by Domenico Candeloro and Anna Rita Sambucini. Abstract: Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the finitely additive case is faced, first assuming uniform $s$-boundedness (without restrictions on the filter), then relaxing this condition but imposing stronger properties on the filter. In order to obtain the last results, a Schur-type convergence theorem is used. Archive classification: math.FA Mathematics Subject Classification: 28B15, 28B05, 06A06, 54F05 Report Number: 0901688 30 jan 2014 Remarks: 18 pages Submitted from: anna.sambucini at unipg.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7818 or http://arXiv.org/abs/1401.7818

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Galicer and Roman Villafane From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:24:46 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Coincidence of extendible vector-valued ideals with their minimal" by Daniel Galicer and Roman Villafane. Abstract: We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if $\mathfrak A$ is an ideal of $n$-linear mappings we give conditions for which the following equality $\mathfrak A(E_1,\dots,E_n;F) = {\mathfrak A}^{min}(E_1,\dots,E_n;F)$ holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis on the space $\mathfrak A(E_1,\dots,E_n;F)$. Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where $\mathfrak A$ is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. For our purposes we also establish a vector-valued version of the Littlewood-Bogdanowicz-Pe{\l}czy\'nski theorem, which we believe is interesting in its own right. Archive classification: math.FA Mathematics Subject Classification: 46G25, 46B22, 46M05, 47H60 Remarks: 25 pages Submitted from: dgalicer at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7896 or http://arXiv.org/abs/1401.7896

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Asuman G. Aksoy and Grzegorz Lewicki From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:26:24 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Minimal projections with respect to numerical radius" by Asuman G. Aksoy and Grzegorz Lewicki. Abstract: In this paper we survey some results on minimality of projections with respect to numerical radius. We note that in the cases $L^p$, $p=1,2,\infty$, there is no difference between the minimality of projections measured either with respect to operator norm or with respect to numerical radius. However, we give an example of a projection from $l^p_3$ onto a two-dimensional subspace which is minimal with respect to norm, but not with respect to numerical radius for $p\neq 1,2,\infty$. Furthermore, utilizing a theorem of Rudin and motivated by Fourier projections, we give a criterion for minimal projections, measured in numerical radius. Additionally, some results concerning strong unicity of minimal projections with respect to numerical radius are given. Archive classification: math.FA Mathematics Subject Classification: Primary 41A35, 41A65, Secondary 47A12 Remarks: 15 pages Submitted from: aaksoy at cmc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0032 or http://arXiv.org/abs/1402.0032

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Emanuel Milman From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:28:18 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On the mean-width of isotropic convex bodies and their associated $L_p$-centroid bodies" by Emanuel Milman. Abstract: For any origin-symmetric convex body $K$ in $\mathbb{R}^n$ in isotropic position, we obtain the bound: \[ M^*(K) \leq C \sqrt{n} \log(n)^2 L_K ~, \] where $M^*(K)$ denotes (half) the mean-width of $K$, $L_K$ is the isotropic constant of $K$, and $C>0$ is a universal constant. This improves the previous best-known estimate $M^*(K) \leq C n^{3/4} L_K$. Up to the power of the $\log(n)$ term and the $L_K$ one, the improved bound is best possible, and implies that the isotropic position is (up to the $L_K$ term) an almost $2$-regular $M$-position. The bound extends to any arbitrary position, depending on a certain weighted average of the eigenvalues of the covariance matrix. Furthermore, the bound applies to the mean-width of $L_p$-centroid bodies, extending a sharp upper bound of Paouris for $1 \leq p \leq \sqrt{n}$ to an almost-sharp bound for an arbitrary $p \geq \sqrt{n}$. The question of whether it is possible to remove the $L_K$ term from the new bound is essentially equivalent to the Slicing Problem, to within logarithmic factors in $n$. Archive classification: math.FA Remarks: 14 pages Submitted from: emanuel.milman at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0209 or http://arXiv.org/abs/1402.0209

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jarno Talponen From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:29:48 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "ODE representation for varying exponent $L^p$ norm" by Jarno Talponen. Abstract: We will construct Banach function space norms arising as weak solutions to ordinary differential equations of first order. This provides as a special case a new way of defining varying exponent $L^p$ spaces, different from the Orlicz type approach. It turns out that the duality of these spaces behaves in an anticipated way, same as the uniform convexity and uniform smoothness. Archive classification: math.FA math.CA Mathematics Subject Classification: 46E30, 46B10, 34A12, 31B10 Submitted from: talponen at iki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0528 or http://arXiv.org/abs/1402.0528

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Trond A. Abrahamsen, Johann Langemets, and Vegard Lima From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 5 Feb 2014 14:31:28 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Almost square Banach spaces" by Trond A. Abrahamsen, Johann Langemets, and Vegard Lima. Abstract: We single out and study a natural class of Banach spaces -- almost square Banach spaces. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i+y\|$ is almost one. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spaces are also studied. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B04, 46B07 Remarks: 22 pages Submitted from: veli at hials.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0818 or http://arXiv.org/abs/1402.0818

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Apostolos Giannopoulos and Emanuel Milman From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:41:11 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "$M$-estimates for isotropic convex bodies and their $L_q$-centroid bodies" by Apostolos Giannopoulos and Emanuel Milman. Abstract: Let $K$ be a centrally-symmetric convex body in $\mathbb{R}^n$ and let $\|\cdot\|$ be its induced norm on ${\mathbb R}^n$. We show that if $K \supseteq r B_2^n$ then: \[ \sqrt{n} M(K) \leqslant C \sum_{k=1}^{n} \frac{1}{\sqrt{k}} \min\left(\frac{1}{r} , \frac{n}{k} \log\Big(e + \frac{n}{k}\Big) \frac{1}{v_{k}^{-}(K)}\right) . \] where $M(K)=\int_{S^{n-1}} \|x\|\, d\sigma(x)$ is the mean-norm, $C>0$ is a universal constant, and $v^{-}_k(K)$ denotes the minimal volume-radius of a $k$-dimensional orthogonal projection of $K$. We apply this result to the study of the mean-norm of an isotropic convex body $K$ in ${\mathbb R}^n$ and its $L_q$-centroid bodies. In particular, we show that if $K$ has isotropic constant $L_K$ then: \[ M(K) \leqslant \frac{C\log^{2/5}(e+ n)}{\sqrt[10]{n}L_K} . \] Archive classification: math.FA Remarks: 19 pages Submitted from: emanuel.milman at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0904 or http://arXiv.org/abs/1402.0904

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Trond A. Abrahamsen, Johann Langemets, Vegard Lima and Olav Nygaard From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:43:08 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Observations on thickness and thinness of Banach spaces" by Trond A. Abrahamsen, Johann Langemets, Vegard Lima and Olav Nygaard. Abstract: The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness. As an example we prove that every Banach space $X$ containing a copy of $c_0$ can be equivalently renormed so that we at the same time have that $c_0$ becomes an M-ideal and both the thickness and thinness index of $X$ equal 1. Archive classification: math.FA Remarks: 8 pages Submitted from: trond.a.abrahamsen at uia.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.0996 or http://arXiv.org/abs/1402.0996

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Szymon Draga From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:44:42 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On weakly locally uniformly rotund norms which are not locally rotund" by Szymon Draga. Abstract: We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund. Archive classification: math.FA Submitted from: szymon.draga at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.1097 or http://arXiv.org/abs/1402.1097

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Goulnara Arzhantseva and Romain Tessera From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:46:30 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Relatively expanding box spaces with no expansion" by Goulnara Arzhantseva and Romain Tessera. Abstract: We exhibit a finitely generated group $G$ and a sequence of finite index normal subgroups $N_n\trianglelefteq G$ such that for every finite generating subset $S\subseteq G$, the sequence of finite Cayley graphs $(G/N_n, S)$ does not coarsely embed into any $L^p$-space for $1\leqslant p<\infty$ (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. Archive classification: math.GR math.FA math.MG Mathematics Subject Classification: 46B85, 20F69, 22D10, 20E22 Remarks: 20 pages Submitted from: goulnara.arjantseva at univie.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.1481 or http://arXiv.org/abs/1402.1481

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Duanxu Dai From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:47:56 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Quantifying (weak) injectivity of a Banach space and its second dual" by Duanxu Dai. Abstract: Let $X$, $Y$ be two Banach spaces. Let $\varepsilon\geq 0$. A mapping $f: X\rightarrow Y$ is said a standard $\varepsilon-$ isometry if $f(0)=0$ and $\|f(x)-f(y)\|-\|x-y\|\leq \eps$. In this paper, we first show that if $X$ is a separable Banach space and $Y^*$ has the point of $w^*$-norm continuity property(in short,$w^*$-PCP), then for every standard $\varepsilon-$ isometry $f:X\rightarrow Y$ there exists a $w^*$-dense $G_\delta$ subset $\Omega$ of $ExtB_{X^*}$ such that there is a bounded linear operator $T: Y\rightarrow C(\Omega,\tau_{w^*})$ with $\|T\|=1$ such that $Tf-Id$ is uniformly bounded by $4\eps$ on $X$. More general results are also given. As a corollary, we obtain quantitative characterizations of injectivity, cardinality injectivity and separably injectivity of a Banach space and its second dual which turn out to give a positive answer to Qian's problem of 1995 in the sense of universality. We also discuss Qian's problem in a $\mathcal{L}_{\infty,\lambda}$-space, $C(K)$-space for a compact Hausdorff space $K$. Moreover, by using some results from Avil$\acute{e}$s-S$\acute{a}$nchez-Castillo-Gonz$\acute{a}$lez- Moreno, Cheng-Dong-Zhang, Johnson-Oikhberg, Rosenthal and Lindenstrauss, estimates for several separably injective Banach spaces are given. Finally, we show a more sharp quantitative and generalized Sobczyk 's theorem. Archive classification: math.FA Mathematics Subject Classification: Primary 46B04, 46B20, 47A58, Secondary 26E25, 54C60, 54C65, 46A20 Remarks: 21 page Submitted from: dduanxu at 163.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2123 or http://arXiv.org/abs/1402.2123

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Alexander Brudnyi From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:49:35 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On near-optimal admissible meshes" by Alexander Brudnyi. Abstract: We show that every compact subset of $\mathbb C^n$ admits a near-optimal admissible mesh. We apply this result to study geometric properties of Banach spaces of traces of real polynomials on $\mathbb R^n$ to compact subsets equipped with supremum norms. Archive classification: math.FA Mathematics Subject Classification: 41A10, 41A17, 65D05 Remarks: 6 pages Submitted from: albru at math.ucalgary.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2303 or http://arXiv.org/abs/1402.2303

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Quanhua Xu From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:51:14 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "$H^\infty$ functional calculus and maximal inequalities for semigroups of contractions on vector-valued $L_p$-spaces" by Quanhua Xu. Abstract: Let $\{T_t\}_{t>0}$ be a strongly continuous semigroup of positive contractions on $L_p(X,\mu)$ with $1<p<\infty$. Let $E$ be a UMD Banach lattice of measurable functions on another measure space $(\Omega,\nu)$. For $f\in L_p(X; E)$ define $$\mathcal M(f)(x, \omega)=\sup_{t>0}\frac1t\Big|\int_0^tT_s(f(\cdot,\omega))(x)ds\Big|,\quad (x,\omega)\in X\times\Omega.$$ Then the following maximal ergodic inequality holds $$\big\|\mathcal M(f)\big\|_{L_p(X; E)}\lesssim \big\|f\big\|_{L_p(X; E)},\quad f\in L_p(X; E).$$ If the semigroup $\{T_t\}_{t>0}$ is additionally assumed to be analytic, then $\{T_t\}_{t>0}$ extends to an analytic semigroup on $L_p(X; E)$ and $\mathcal M(f)$ in the above inequality can be replaced by the following sectorial maximal function $$\mathcal T_\theta(f)(x, \omega)=\sup_{|{\rm arg}(z)|<\theta}\big|T_z(f(\cdot,\omega))(x)\big|$$ for some $\theta>0$. Under the latter analyticity assumption and if $E$ is a complex interpolation space between a Hilbert space and a UMD Banach space, then $\{T_t\}_{t>0}$ extends to an analytic semigroup on $L_p(X; E)$ and its negative generator has a bounded $H^\infty(\Sigma_\sigma)$ calculus for some $\sigma<\pi/2$. Archive classification: math.FA Mathematics Subject Classification: Primary: 47A35, 47A60. Secondary: 46B20, 42B25 Submitted from: quanhua.xu at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2344 or http://arXiv.org/abs/1402.2344

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Joanna Garbulinska - Wegrzyn From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:52:59 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "An isometrically universal Banach space with a monotone Schauder" by Joanna Garbulinska - Wegrzyn. Abstract: We present an isometric version of the complementably universal Banach space $\mathcal{B}$ with a monotone Schauder basis. The space $\mathcal{B}$ is isomorphic to Pe\l czy\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B04. Secondary: 46M15, 46M40 Remarks: 10 pages Submitted from: jgarbulinska at ujk.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2660 or http://arXiv.org/abs/1402.2660

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel J. Fresen and Richard A. Vitale From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:54:25 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Concentration of random polytopes around the expected convex hull" by Daniel J. Fresen and Richard A. Vitale. Abstract: We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a corresponding strong law of large numbers. Archive classification: math.PR math.FA Mathematics Subject Classification: 60D05, 60F99, 52A20, 52A22, 52B11 Remarks: 8 pages Submitted from: daniel.fresen at yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2718 or http://arXiv.org/abs/1402.2718

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikko Kemppainen From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:55:58 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators" by Mikko Kemppainen. Abstract: In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X). Archive classification: math.FA Mathematics Subject Classification: 42B35 (Primary), 46E40 (Secondary) Remarks: 19 pages Submitted from: mikko.k.kemppainen at helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.2886 or http://arXiv.org/abs/1402.2886

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Schuett and E. M. Werner From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 21 Feb 2014 13:59:47 -0600 (CST) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Functional versions of L_p-affine surface area and entropy" by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec, C. Schuett and E. M. Werner. Abstract: In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the L_p-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original L_p-affine surface area. We prove duality relations and affine isoperimetric inequalities for log concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities. Archive classification: math.FA 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/1402.3250 or http://arXiv.org/abs/1402.3250

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Second Announcement - BWB 2014 From: valentin ferenczi <ferenczi.math at gmail.com> Date: Tue, 25 Feb 2014 11:00:35 -0300 (08:00 CST) To: banach at math.okstate.edu

2nd ANNOUNCEMENT OF BWB 2014 First Brazilian Workshop in Geometry of Banach Spaces August 25-29, 2014 Maresias, São Paulo State, Brazil. This is the 2nd announcement for the First Brazilian Workshop in Geometry of Banach Spaces, organized by the University of São Paulo (USP), in the week August 25-29, 2014. This international conference will take place at the Beach Hotel Maresias, on the coast of São Paulo State, in Maresias. The scientific program will focus on the theory of geometry of Banach spaces, with emphasis on the following directions: linear theory of infinite dimensional spaces and its relations to Ramsey theory, homological theory and set theory; nonlinear theory; and operator theory. Registration and abstract submissions are now open on the website of conference: http://www.ime.usp.br/~banach/bwb2014/ Deadline for registration is June 30th and for abstract submission is April 30th. Please consult the website for all information and contact us at bwb2014 at gmail.com if you have any question. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) J. M. F. Castillo (U. Extremadura) P. Dodos (U. Athens) G. Godefroy (Paris 6) R. Haydon (U. Oxford) W. B. Johnson (Texas A&M) P. Koszmider (Polish Acad. Warsaw) G. Pisier (Paris 6 & Texas A&M) C. Rosendal (U. Illinois Chicago) G. Schechtman (Weizmann Inst.) Th. Schlumprecht (Texas A&M) S. Todorcevic (Paris 7 & U. Toronto) Scientific committee J. M. F. Castillo (U. Extremadura) V. Ferenczi (U. São Paulo, chair) R. Haydon (U. Oxford) W. B. Johnson (Texas A&M) G. Pisier (Paris 6 & Texas A&M) Th. Schlumprecht (Texas A&M) S. Todorcevic (Paris 7 & U. Toronto) The organizers, F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Integration, Vector Measures and Related Topics VI - a reminder From: Grzegorz Plebanek <Grzegorz.Plebanek at math.uni.wroc.pl> Date: Tue, 25 Feb 2014 19:24:46 +0100 (CET) To: banach at math.okstate.edu

This is a reminder about the conference THE MEETING: Integration, Vector Measures and Related Topics VI WHEN: June 15 - 21, 2014 WHERE: the Mathematical Research and Conference Center in Bedlewo (near Poznan, Poland), REGISTRATION and more information on the conference webpage: http://www.math.uni.wroc.pl/~drygier/ivmrt2014/ INVITED SPEAKERS: Antonio Aviles (Murcia), Erik J. Balder (Utrecht), Oscar Blasco (Valencia), Guillermo Curbera (Sevilla), Luisa Di Piazza (Palermo), Harold Garth Dales (Lancaster) Joe Diestel (Kent), Marian Fabian (Prague), David H. Fremlin (Colchester), Ondrej Kalenda (Prague), Zbigniew Lipecki (Wrocaw), Jose Rodriguez (Murcia) The organizing committee: M. Balcerzak, M. Cichon, K. Musial, G. Plebanek _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> From: Dale Alspach <alspach at math.okstate.edu> Subject: [Banach] Piotr Mankiewicz Date: Wed, 26 Feb 2014 19:00:22 -0600

With a deep regret we have to inform that Piotr Mankiewicz suddenly passed away on February 21, 2014. We lost a good friend and a good mathematician. He will be missed. If you would like to send a few words to his family please send it to his daughter Ania, at annamankiewicz at gmail.com Nicole Tomczak-Jaegermann _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Vladimir P. Fonf and Clemente Zanco From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:49:29 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Almost overcomplete and almost overtotal sequences in Banach spaces" by Vladimir P. Fonf and Clemente Zanco. Abstract: The new concepts are introduced of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such sequences is relatively norm-compact and we obtain several applications of this fact. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B50, 46B45 Submitted from: clemente.zanco at unimi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.6247 or http://arXiv.org/abs/1402.6247

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Despoina Zisimopoulou From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:52:10 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Bourgain-Delbaen $\mathcal{L}^{\infty}$-sums of Banach spaces" by Despoina Zisimopoulou. Abstract: Motivated by a problem stated by S.A.Argyros and Th. Raikoftsalis, we introduce a new class of Banach spaces. Namely, for a sequence of separable Banach spaces $(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$, we define the Bourgain Delbaen $\mathcal{L}^{\infty}$-sum of the sequence $(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$ which is a Banach space $\mathcal{Z}$ constructed with the Bourgain-Delbaen method. In particular, for every $1\leq p<\infty$, taking $X_n=\ell_p$ for every $n\in\mathbb{N}$ the aforementioned space $\mathcal{Z}_p$ is strictly quasi prime and admits $\ell_p$ as a complemented subspace. We study the operators acting on $\mathcal{Z}_p$ and we prove that for every $n\in\mathbb{N}$, the space $\mathcal{Z}^n_p=\sum_{i=1}^n\oplus \mathcal{Z}_p$ admits exactly $n+1$, pairwise not isomorphic, complemented subspaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B25, 46B28 Remarks: 29 pages, no figures Submitted from: dzisimopoulou at hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1402.6564 or http://arXiv.org/abs/1402.6564

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by A. Elbour, N. Machrafi, and M. Moussa From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:53:54 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On the class of weak almost limited operators" by A. Elbour, N. Machrafi, and M. Moussa. Abstract: We introduce and study the class of weak almost limited operators. We establish a characterization of pairs of Banach lattices $E$, $F$ for which every positive weak almost limited operator $T:E\rightarrow F$ is almost limited (resp. almost Dunford-Pettis). As consequences, we will give some interesting results. Archive classification: math.FA Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary) Submitted from: azizelbour at hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.0136 or http://arXiv.org/abs/1403.0136

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Claudia Correa and Daniel V. Tausk From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:55:17 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On the $c_0$-extension property for compact lines" by Claudia Correa and Daniel V. Tausk. Abstract: We present a characterization of the continuous increasing surjections $\phi:K\to L$ between compact lines $K$ and $L$ for which the corresponding subalgebra $\phi^*C(L)$ has the $c_0$-extension property in $C(K)$. A natural question arising in connection with this characterization is shown to be independent of the axioms of ZFC. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46E15, 54F05 Remarks: 12 pages Submitted from: tausk at ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.0605 or http://arXiv.org/abs/1403.0605

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Ioannis Gasparis From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:56:38 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A proof of Rosenthal's \(\ell_1\) Theorem" by Ioannis Gasparis. Abstract: A proof is given of Rosenthal's \(\ell_1\) theorem. Archive classification: math.FA Mathematics Subject Classification: 46B03 Remarks: 5 pages Submitted from: ioagaspa at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.1163 or http://arXiv.org/abs/1403.1163

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Anna Kaminska, Karol Lesnik, and Yves Raynaud From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 14:58:42 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Dual spaces to Orlicz - Lorentz spaces" by Anna Kaminska, Karol Lesnik, and Yves Raynaud. Abstract: For an Orlicz function $\varphi$ and a decreasing weight $w$, two intrinsic exact descriptions are presented for the norm in the K\"othe dual of an Orlicz-Lorentz function space $\Lambda_{\varphi,w}$ or a sequence space $\lambda_{\varphi,w}$, equipped with either Luxemburg or Amemiya norms. The first description of the dual norm is given via the modular $\inf\{\int\varphi_*(f^*/|g|)|g|: g\prec w\}$, where $f^*$ is the decreasing rearrangement of $f$, $g\prec w$ denotes the submajorization of $g$ by $w$ and $\varphi_*$ is the complementary function to $\varphi$. The second one is stated in terms of the modular $\int_I \varphi_*((f^*)^0/w)w$, where $(f^*)^0$ is Halperin's level function of $f^*$ with respect to $w$. That these two descriptions are equivalent results from the identity $\inf\{\int\psi(f^*/|g|)|g|: g\prec w\}=\int_I \psi((f^*)^0/w)w$ valid for any measurable function $f$ and Orlicz function $\psi$. Analogous identity and dual representations are also presented for sequence spaces. Archive classification: math.FA Mathematics Subject Classification: 42B25, 46B10, 46E30 Remarks: 25 pages Submitted from: klesnik at vp.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.1505 or http://arXiv.org/abs/1403.1505

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Deping Ye From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 10 Mar 2014 15:00:17 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "New Orlicz affine isoperimetric inequalities" by Deping Ye. Abstract: The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many results in the $L_p$-Brunn-Minkowski theory have been extended to their Orlicz counterparts. The aim of this paper is to develop Orlicz $L_{\phi}$ affine and geominimal surface areas for single convex body as well as for multiple convex bodies, which generalize the $L_p$ (mixed) affine and geominimal surface areas -- fundamental concepts in the $L_p$-Brunn-Minkowski theory. Our extensions are different from the general affine surface areas by Ludwig (in Adv. Math. 224 (2010)). Moreover, our definitions for Orlicz $L_{\phi}$ affine and geominimal surface areas reveal that these affine invariants are essentially the infimum/supremum of $V_{\phi}(K, L^\circ)$, the Orlicz $\phi$-mixed volume of $K$ and the polar body of $L$, where $L$ runs over all star bodies and all convex bodies, respectively, with volume of $L$ equal to the volume of the unit Euclidean ball $B_2^n$. Properties for the Orlicz $L_{\phi}$ affine and geominimal surface areas, such as, affine invariance and monotonicity, are proved. Related Orlicz affine isoperimetric inequalities are also established. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A20, 53A15 Submitted from: deping.ye at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.1643 or http://arXiv.org/abs/1403.1643

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 13:53:26 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by B. Bongiorno, U. B. Darju, and L. Di Piazza

This is an announcement for the paper "Lineability of non-differentiable Pettis primitives" by B. Bongiorno, U. B. Darju, and L. Di Piazza. Abstract: Let X be an in?nite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued Pettis integrable function on [0; 1] whose primitive is nowhere weakly di?erentiable. Using their technique and some new ideas we show that ND, the set of strongly measurable Pettis integrable functions with nowhere weakly di?erentiable primitives, is lineable, i.e., there is an in?nite dimensional vector space whose nonzero vectors belong to ND. Archive classification: math.FA Mathematics Subject Classification: 46G10, 28B05 Submitted from: ubdarj01 at louisville.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.1908 or http://arXiv.org/abs/1403.1908

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 13:55:47 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Sheng Zhang

This is an announcement for the paper "Coarse quotient mappings between metric spaces" by Sheng Zhang. Abstract: We give a definition of coarse quotient mapping and show that several results for uniform quotient mapping also hold in the coarse setting. In particular, we prove that any Banach space that is a coarse quotient of $L_p\equiv L_p[0,1]$, $1<p<\infty$, is isomorphic to a linear quotient of $L_p$. It is also proved that $\ell_q$ is not a coarse quotient of $\ell_p$ for $1<p<q<\infty$ using Rolewicz's property ($\beta$). Archive classification: math.FA math.MG Submitted from: z1986s at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.1934 or http://arXiv.org/abs/1403.1934

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 13:58:14 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Jan-David Hardtke

This is an announcement for the paper "WORTH property, Garc\'{i}a-Falset coefficient and Opial property of infinite sums" by Jan-David Hardtke. Abstract: We prove some results concerning the WORTH property and the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. The Opial property/uniform Opial property of infinite $\ell^p$-sums is also studied and some properties analogous to the Opial property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\mu,X)$ are discussed. Archive classification: math.FA Mathematics Subject Classification: 46B20 46E40 Remarks: 22 pages Submitted from: hardtke at math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.2647 or http://arXiv.org/abs/1403.2647

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:00:20 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by A. Elbour, N. Machrafi, and M. Moussa

This is an announcement for the paper "Weak compactness of almost limited operators" by A. Elbour, N. Machrafi, and M. Moussa. Abstract: The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma $-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F $ is weakly compact if and only if $E$ is reflexive or the norm of $F$ is order continuous. Also, we show that if $E$ is a $\sigma $-Dedekind complete Banach lattice then the square of every positive almost limited operator $ T:E\rightarrow E$ is weakly compact if and only if the norm of $E$ is order continuous. Archive classification: math.FA Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65 (Secondary) Remarks: 5 pages Submitted from: azizelbour at hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3348 or http://arXiv.org/abs/1403.3348

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:02:59 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Dustin G. Mixon

This is an announcement for the paper "Explicit matrices with the Restricted Isometry Property: Breaking the square-root bottleneck" by Dustin G. Mixon. Abstract: Matrices with the restricted isometry property (RIP) are of particular interest in compressed sensing. To date, the best known RIP matrices are constructed using random processes, while explicit constructions are notorious for performing at the "square-root bottleneck," i.e., they only accept sparsity levels on the order of the square root of the number of measurements. The only known explicit matrix which surpasses this bottleneck was constructed by Bourgain, Dilworth, Ford, Konyagin and Kutzarova. This chapter provides three contributions to further the groundbreaking work of Bourgain et al.: (i) we develop an intuition for their matrix construction and underlying proof techniques; (ii) we prove a generalized version of their main result; and (iii) we apply this more general result to maximize the extent to which their matrix construction surpasses the square-root bottleneck. Archive classification: math.FA cs.IT math.CO math.IT Remarks: Book chapter, submitted to Compressed Sensing and its Applications Submitted from: dustin.mixon at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3427 or http://arXiv.org/abs/1403.3427

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:05:20 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Ralf Beckmann and Anton Deitmar

This is an announcement for the paper "Two application of nets" by Ralf Beckmann and Anton Deitmar. Abstract: Two applications of nets are given. The first is an extension of the Bochner integral to arbitrary locally convex spaces, leading to an integration theorye of more general vector valued functions then in the classical approach by Gelfand and Pettis. The second application starts with the observation that an operator on a Hilbert space is trace class if and only if the net of ``principal trace minors'' converges. The notion of a ``determinant class operator'' then is defined as one for which the net of determinantal principal minors converges. It is shown that for a normal operator A this condition coincides with 1-A being trace class. Archive classification: math.FA Submitted from: deitmar at uni-tuebingen.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.3207 or http://arXiv.org/abs/1403.3207

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:08:02 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by S. J. Dilworth, D. Kutzarova, E. Odell, Th. Sch ***lumprecht and A. Zsak

This is an announcement for the paper "Renorming spaces with greedy bases" by S. J. Dilworth, D. Kutzarova, E. Odell, Th. Schlumprecht and A. Zsak. Abstract: We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given $\vare>0$, so that the basis becomes $(1+\vare)$-democratic, and hence $(2+\vare)$-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is $(1+\vare)$-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in $L_p[0,1]$, $1<p<\infty$, and in dyadic Hardy space $H_1$, as well as the unit vector basis of Tsirelson space. Archive classification: math.FA Mathematics Subject Classification: 41A65, 41A44, 41A50, 46B03 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/1403.3777 or http://arXiv.org/abs/1403.3777

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:10:10 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by F. Baudier, D. Freeman, Th. Schlumprecht and A. *** Zsak

This is an announcement for the paper "The metric geometry of the Hamming cube and applications" by F. Baudier, D. Freeman, Th. Schlumprecht and A. Zsak. Abstract: The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the $C(K)$-distortion of important classes of separable Banach spaces, where $K$ is a countable compact space in the family $ \{ [0,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot n],\dots,[0,\omega^\omega]\}\ ,$ are obtained. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B85 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/1403.4376 or http://arXiv.org/abs/1403.4376

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:12:28 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Marek Cuth and Ondrej F.K. Kalenda

This is an announcement for the paper "Monotone retractability and retractional skeletons" by Marek Cuth and Ondrej F.K. Kalenda. Abstract: We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a question of R. Rojas-Hern{\'a}ndez and V. V. Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W. Kubi\'s. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C15, 54D30, 46B26 Remarks: 14 pages Submitted from: kalenda at karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4480 or http://arXiv.org/abs/1403.4480

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:15:10 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by Daniel Carando, Veronica Dimant, Pablo Sevilla- ***Peris and Roman Villafane

This is an announcement for the paper "Diagonal extendible multilinear operators between $\ell_p$-spaces" by Daniel Carando, Veronica Dimant, Pablo Sevilla-Peris and Roman Villafane. Abstract: We study extendibility of diagonal multilinear operators from $\ell_p$ to $\ell_q$ spaces. We determine the values of $p$ and $q$ for which every diagonal $n$-linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on $\ell_p$. Archive classification: math.FA Mathematics Subject Classification: 47H60, 46B45, 46G25 Submitted from: rvillafa at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4577 or http://arXiv.org/abs/1403.4577

Return-path: <alspach at math.okstate.edu> Date: Sun, 30 Mar 2014 14:20:09 CDT To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) Subject: Abstract of a paper by C. Angosto, M. C. Listan-Garcia, and F. Rambla- ***Barreno

This is an announcement for the paper "Continuity properties of sequentially asymptotically center-complete spaces" by C. Angosto, M. C. Listan-Garcia, and F. Rambla-Barreno. Abstract: We obtain formulae to calculate the asymptotic center and radius of bounded sequences in ${\cal C}_0(L)$ spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a H\"older-type estimation is given. Archive classification: math.FA Mathematics Subject Classification: 41A50 (Primary) 46E15 (Secondary) Submitted from: fernando.rambla at uca.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4646 or http://arXiv.org/abs/1403.4646

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski From: Jose Rodriguez <joserr at um.es> Date: Wed, 02 Apr 2014 08:53:24 +0200 To: banach at math.okstate.edu

Dear colleagues: This is the third announcement of the conference Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski which will be held in Albacete (Spain) on June 10-13, 2014, on the occasion of the 70th birthday of Stanimir Troyanski. The deadline for early registration is April 30. Our web page at https://sites.google.com/site/geometryofbanachspaces/ contains detailed information about the conference, including: registration and payment, abstract submission, accommodation and travel. Main speakers who accepted our invitation are: S. Argyros, J. Castillo, S. Dilworth, M. Fabian, V. Fonf, P. Hajek, R. Haydon, F. Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, J. Revalski, T. Schlumprecht, R. Smith, A. Suarez Granero. In addition, participants will have the opportunity to deliver a short talk. Please do not hesitate in contacting us at geometry.banach.spaces.2014 at gmail.com if you need further information. Looking forward to meeting you! The organizers, A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Workshop at Texas A&M From: Bill Johnson <johnson at math.tamu.edu> Date: Thu, 10 Apr 2014 13:56:33 -0500 (CDT) To: banach at math.okstate.edu

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2014 The Summer 2014 Workshop in Analysis and Probability at Texas A&M University will be in session from July 1 to 31, 2014. All activities will take place in the Blocker Building. The homepage of the Workshop can be found at http://www.math.tamu.edu/~kerr/workshop The Summer Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held July 25-27. July 21-25 there will be a Concentration Week on "Free Probability", organized by Michael Anshelevich, Ken Dykema, and John Williams. This meeting aims both to introduce younger researchers to this fast-growing field and to showcase the latest results. Topics discussed will include operator algebras, connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The homepage can be found at http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 Also, June 9-13 there will be a Concentration Week on "Groups, Groupoids, and Dynamics" organized by David Kerr and Volodymyr Nekrashevych (note the special dates, which fall outside the scope of the main Workshop period). This meeting aims to provide a forum for understanding and exploring various recent developments in groups and dynamics that revolve around groupoids and equivalence relations. Topics will include topological orbit equivalence, amenability, hyperbolicity, self-similar groups, entropy, and rigidity in measurable group theory. Lectures series will be given by Lewis Bowen and Thierry Giordano. The homepage can be found at http://www.math.tamu.edu/~kerr/concweek14 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>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. For information about the Concentration Week on "Free Probability" contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema <ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu> For information about the Concentration Week on "Groups, Groupoids, Dynamics" contact David Kerr <kerr at math.tamu.edu> or Volodymyr Nekrashevych <nekrash at math.tamu.edu>. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Oleg Reinov From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:10:58 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Some thoughts on approximation properties" by Oleg Reinov. Abstract: We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the properties like the $AP_s$ or $AP_{(s,w)}$ for $s\in (0,1],$ which give us the possibility to identify the spaces of $s$-nuclear and $(s,w)$-nuclear operators with the corresponding tensor products (e.g., related to Lorentz sequence spaces). Some applications are given (in particular, we present not difficult proofs of the trace-formulas of Grothendieck-Lidskii type for several ideals of nuclear operators). Archive classification: math.FA Mathematics Subject Classification: 46B28 Spaces of operators, tensor products, approximation Remarks: 17 pages. A talk at "July 22-26 Positivity 2013 Holland, Leiden" Submitted from: orein51 at mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.4746 or http://arXiv.org/abs/1403.4746

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Gustavo Araujo and Daniel Pellegrino From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:12:32 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Spaceability and optimal estimates for summing multilinear operators" by Gustavo Araujo and Daniel Pellegrino. Abstract: We show that given a positive integer $m$, a real number $p\in\left[ 2,\infty\right) $ and $1\leq s<p^{\ast}$ the set of non--multiple $\left( r,s\right) $--summing $m$--linear forms on $\ell_{p}\times\cdots\times\ell_{p}$ is spaceable whenever $r<\frac{2ms}{s+2m-ms}$. This result is optimal since for $r\geq\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\ell _{p}\times\cdots\times\ell_{p}$ are multiple $\left( r,s\right) $--summing. Among other results, we improve some results from \cite{laa} and generalize a result related to cotype (from 2010) due to Botelho, Michels and the second named author. We also prove some new coincidence results for the class of absolutely summing multilinear operators. Archive classification: math.FA Submitted from: pellegrino at pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6064 or http://arXiv.org/abs/1403.6064

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Carando and Martin Mazzitelli From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:13:59 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Bounded holomorphic functions attaining their norms in the bidual" by Daniel Carando and Martin Mazzitelli. Abstract: Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(\beta)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases where our results apply. Archive classification: math.FA Submitted from: mmazzite at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6431 or http://arXiv.org/abs/1403.6431

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Cedric Arhancet From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:15:24 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On a conjecture of Pisier on the analyticity of semigroups" by Cedric Arhancet. Abstract: We show that the analyticity of some semigroups $(T_t)_{t \geq 0}$ of contractive Fourier multipliers on $L^p$-spaces of compact abelian groups is preserved by the tensorisation of the identity operator of a Banach space for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. We also give versions of this result for some semigroups of Schur multipliers and Fourier multipliers on noncommutative $L^p$-spaces. Finally, we give a precise description of semigroups of Schur multipliers to which the result of this paper can be applied. Archive classification: math.FA Remarks: 10 pages; comments are welcome Submitted from: cedric.arhancet at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6737 or http://arXiv.org/abs/1403.6737

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Pedro Levit Kaufmann From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:16:46 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Products of Lipschitz-free spaces and applications" by Pedro Levit Kaufmann. Abstract: We show that, given a Banach space $X$, the Lipschitz-free space over $X$, denoted by $\mathcal{F}(X)$, is isomorphic to $(\sum_{n=1}^\infty \mathcal{F}(X))_{\ell_1}$. Some applications are presented, including a non-linear version of Pe\l czy\'ski's decomposition method for Lipschitz-free spaces and the identification up to isomorphism between $\mathcal{F}(\mathbb{R}^n)$ and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into $\mathbb{R}^n$ and which contains a subset that is Lipschitz equivalent to the unit ball of $\mathbb{R}^n$. We also show that $\mathcal{F}(M)$ is isomorphic to $\mathcal{F}(c_0)$ for all separable metric spaces $M$ which are absolute Lipschitz retracts and contain a subset which is Lipschitz equivalent to the unit ball of $c_0$. This class contains all $C(K)$ spaces with $K$ infinite compact metric (Dutrieux and Ferenczi had already proved that $\mathcal{F}(C(K))$ is isomorphic to $\mathcal{F}(c_0)$ for those $K$ using a different method). Finally we study Lipschitz-free spaces over certain unions and quotients of metric spaces, extending a result by Godard. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46T99 Remarks: 17 pages, 1 figure Submitted from: pkaufmann at math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6605 or http://arXiv.org/abs/1403.6605

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mehdi Ghasemi From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:18:11 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Integral representation of linear functionals on function spaces" by Mehdi Ghasemi. Abstract: Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be representable as an integral with respect to a measure $\mu$ on $X$ such that elements of $\mathcal{A}$ are $\mu$-measurable. This general result then is applied to the case where $X$ carries a topological structure and $A$ is a family of continuous functions and naturally $\mathcal{A}$ is the Borel structure of $X$. As an application, short solutions for the full and truncated $K$-moment problem are presented. An analogue of Riesz-Markov-Kakutani representation theorem is given where $C_{c}(X)$ is replaced with whole $C(X)$. Then we consider the case where $A$ only consists of bounded functions and hence is equipped with $\sup$-norm. Archive classification: math.FA Mathematics Subject Classification: 47A57, 28C05, 28E99 Submitted from: mehdi.ghasemi at usask.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6956 or http://arXiv.org/abs/1403.6956

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:19:32 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A note on a Bohnenblust-Hille-Helson type inequality" by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris. Abstract: We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree. Archive classification: math.FA Submitted from: psevilla at mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.7033 or http://arXiv.org/abs/1403.7033

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Arnaud Marsiglietti From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:21:07 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On improvement of the concavity of convex measures" by Arnaud Marsiglietti. Abstract: We prove that a general class of measures, which includes $\log$-concave measures, are $\frac{1}{n}$-concave in the terminology of Borell under additional assumptions on the measure or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch. Archive classification: math.FA Submitted from: arnaud.marsiglietti at univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.7643 or http://arXiv.org/abs/1403.7643

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by O. Blasco, G. Botelho, D, Pellegrino, and P. Rueda From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:22:43 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Absolutely summing multilinear operators on $\ell_p$ spaces" by O. Blasco, G. Botelho, D, Pellegrino, and P. Rueda. Abstract: We prove new summability properties for multilinear operators on $\ell_p$ spaces. An important tool for this task is a better understanding of the interplay between almost summing and absolutely summing multilinear operators. Archive classification: math.FA Submitted from: pellegrino at pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.1322 or http://arXiv.org/abs/1404.1322

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:24:23 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "An introduction to Nigel Kalton's work on differentials of complex interpolation processes for Kothe spaces" by Michael Cwikel, Mario Milman and Richard Rochberg. Abstract: This paper contains no new results. It is intended to be merely a brief introduction to the long paper: N. J. Kalton, Differentials of complex interpolation processes for Kothe function spaces. Trans. Amer. Math. Soc. 333 (1992), no. 2, 479--529. and to mention some possible directions for applying the powerful methods developed in Kalton's paper for further future research. The reader should also be aware of other perspectives in other commentaries on Kalton's paper, which appear in other sources to which we refer. Archive classification: math.FA Mathematics Subject Classification: 46B70 (Primary), 42B20, 42B30, 42B35, 46B42 (Secondary) Remarks: 12 pages 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/1404.2893 or http://arXiv.org/abs/1404.2893

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jan van Neerven, Mark Veraar, and Lutz Weis From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:30:15 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On the R-boundedness of stochastic convolution operators" by Jan van Neerven, Mark Veraar, and Lutz Weis. Abstract: The $R$-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal $L^p$-regularity, $2<p<\infty$, for certain classes of sectorial operators acting on spaces $X=L^q(\mu)$, $2\le q<\infty$. This paper presents a systematic study of $R$-boundedness of such families. Our main result generalises the afore-mentioned $R$-boundedness result to a larger class of Banach lattices $X$ and relates it to the $\ell^{1}$-boundedness of an associated class of deterministic convolution operators. We also establish an intimate relationship between the $\ell^{1}$-boundedness of these operators and the boundedness of the $X$-valued maximal function. This analysis leads, quite surprisingly, to an example showing that $R$-boundedness of stochastic convolution operators fails in certain UMD Banach lattices with type $2$. Archive classification: math.FA math.PR Mathematics Subject Classification: Primary: 60H15, Secondary: 42B25, 46B09, 46E30, 60H05 Submitted from: m.c.veraar at tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.3353 or http://arXiv.org/abs/1404.3353

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Aude Dalet From: alspach at math.okstate.edu (Dale Alspach) Date: Wed, 16 Apr 2014 14:31:39 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Free spaces over some proper metric spaces" by Aude Dalet. Abstract: We prove that the Lipschitz-free space over a countable proper metric space and over a proper ultrametric space is isometric to a dual space and has the metric approximation property. Archive classification: math.FA Mathematics Subject Classification: 46B10, 46B28 Submitted from: aude.dalet at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.3939 or http://arXiv.org/abs/1404.3939 ubject: Abstract of a paper by Rui F. Vigelis and Charles C. Cavalcante From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:30:52 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu This is an announcement for the paper "Smoothness of the Orlicz Norm in Musielak-Orlicz Function Spaces" by Rui F. Vigelis and Charles C. Cavalcante. Abstract: In this paper, we present a characterization of support functionals and smooth points in $L_{0}^{\Phi}$, the Musielak-Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of $L_{0}^{\Phi}$ is also obtained. Some expressions involving the norms of functionals in $(L_{0}^{\Phi})^{*}$, the topological dual of $L_{0}^{\Phi}$, are proved for arbitrary Musielak-Orlicz functions. Archive classification: math.FA Submitted from: rfvigelis at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.4306 or http://arXiv.org/abs/1404.4306

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by N. Albuquerque, D. Nunez-Alarcon, J. Santos and D. M. Serrano-Rodriguez From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:34:50 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Absolutely summing multilinear operators via interpolation" by N. Albuquerque, D. Nunez-Alarcon, J. Santos and D. M. Serrano-Rodriguez. Abstract: We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the multilinear Bohnenblust-Hille constants due to F. Bayart, D. Pellegrino and J. Seoane-Sep\'ulveda. More precisely, as a consequence of our main result, for $1\leq t<2$ and $m\in \mathbb{N}$ we prove that $$ \left( \sum_{i_{1},\dots ,i_{m}=1}^{\infty }\left\vert U\left(e_{i_{1}},\dots ,e_{i_{m}}\right) \right\vert^{\frac{2tm}{2+(m-1)t}}\right)^{\frac{2+(m-1)t}{2tm}} \leq \left[\prod_{j=2}^{m}\Gamma \left( 2-\frac{2-t}{jt-2t+2}\right) ^{\frac{t(j-2)+2}{2t-2jt}}\right] \left\Vert U\right\Vert $$ for all complex $m$-linear forms $U:c_{0}\times \cdot \cdot \cdot \times c_{0}\rightarrow \mathbb{C}$. Archive classification: math.FA Submitted from: ngalbqrq at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.4949 or http://arXiv.org/abs/1404.4949

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Grigoris Paouris and Petros Valettas From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:36:37 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Neighborhoods on the Grasmannian of marginals with bounded isotropic constant" by Grigoris Paouris and Petros Valettas. Abstract: We show that for any isotropic log-concave probability measure $\mu$ on $\mathbb R^n$, for every $\varepsilon > 0$, every $1 \leq k \leq \sqrt{n}$ and any $E \in G_{n,k}$ there exists $F \in G_{n,k}$ with $d(E,F) < \varepsilon$ and $L_{\pi_F\mu} < C/\varepsilon$. Archive classification: math.FA Submitted from: petvalet at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.4988 or http://arXiv.org/abs/1404.4988

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by David Alonso-Gutierrez, Markus Passenbrunner and Joscha Prochno From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:38:08 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Probabilistic estimates for tensor products of random vectors" by David Alonso-Gutierrez, Markus Passenbrunner and Joscha Prochno. Abstract: We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$. Archive classification: math.FA Mathematics Subject Classification: 46B09, 46B07, 46B28, 46B45 Remarks: 14 pages Submitted from: joscha.prochno at jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.5423 or http://arXiv.org/abs/1404.5423

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Anna Kamont and Markus Passenbrunner From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:39:55 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Unconditionality of orthogonal spline systems in $H^1$" by Anna Kamont and Markus Passenbrunner. Abstract: We give a simple geometric characterization of knot sequences for which the corresponding orthonormal spline system of arbitrary order $k$ is an unconditional basis in the atomic Hardy space $H^1[0,1]$. Archive classification: math.FA Remarks: 31 pages Submitted from: markus.passenbrunner at jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.5493 or http://arXiv.org/abs/1404.5493

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Luis Rademacher From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:41:14 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A simplicial polytope that maximizes the isotropic constant must be a simplex" by Luis Rademacher. Abstract: The isotropic constant $L_K$ is an affine-invariant measure of the spread of a convex body $K$. For a $d$-dimensional convex body $K$, $L_K$ can be defined by $L_K^{2d} = \det(A(K))/(\mathrm{vol}(K))^2$, where $A(K)$ is the covariance matrix of the uniform distribution on $K$. It is an outstanding open problem to find a tight asymptotic upper bound of the isotropic constant as a function of the dimension. It has been conjectured that there is a universal constant upper bound. The conjecture is known to be true for several families of bodies, in particular, highly symmetric bodies such as bodies having an unconditional basis. It is also known that maximizers cannot be smooth. In this work we study the gap between smooth bodies and highly symmetric bodies by showing progress towards reducing to a highly symmetric case among non-smooth bodies. More precisely, we study the set of maximizers among simplicial polytopes and we show that if a simplicial $d$-polytope $K$ is a maximizer of the isotropic constant among $d$-dimensional convex bodies, then when $K$ is put in isotropic position it is symmetric around any hyperplane spanned by a $(d-2)$-dimensional face and the origin. By a result of Campi, Colesanti and Gronchi, this implies that a simplicial polytope that maximizes the isotropic constant must be a simplex. Archive classification: math.FA math.MG math.PR Submitted from: lrademac at cse.ohio-state.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.5662 or http://arXiv.org/abs/1404.5662

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Zakhar Kabluchko and Dmitry Zaporozhets From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:45:00 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Intrinsic volumes of Sobolev balls" by Zakhar Kabluchko and Dmitry Zaporozhets. Abstract: A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first intrinsic volumes of infinite-dimensional convex compact sets including unit balls with respect to Sobolev-type seminorms and ellipsoids in the Hilbert space. We relate the distribution of the random one-dimensional projections of these sets to the distributions $S_1,S_2,C_1,C_2$ studied by Biane, Pitman, Yor [Bull. AMS 38 (2001)]. We show that the $k$-th intrinsic volume of the set of all functions on $[0,1]$ which have Lipschitz constant bounded by $1$ and which vanish at $0$ (respectively, which have vanishing integral) is given by $$ V_k = \frac{\pi^{k/2}}{\Gamma\left(\frac 32 k +1 \right)}, \text{ respectively } V_k = \frac{\pi^{(k+1)/2}}{2\Gamma\left(\frac 32 k +\frac 32\right)}. $$ This is related to the results of Gao and Vitale [Discrete Comput. Geom.} 26 (2001), Elect. Comm. Probab. 8 (2003)] who considered a similar question for functions with a restriction on the total variation instead of the Lipschitz constant. Using the results of Gao and Vitale we give a new proof of the formula for the expected volume of the convex hull of the $d$-dimensional Brownian motion which is due to Eldan [Elect. J. Probab., to appear]. Additionally, we prove an analogue of Eldan's result for the Brownian bridge. Similarly, we show that the results on the intrinsic volumes of the Lipschitz balls can be translated into formulae for the expected volumes of zonoids (Aumann integrals) generated by the Brownian motion and the Brownian bridge. Our proofs exploit Sudakov's and Tsirelson's theorems which establish a connection between the intrinsic volumes and the isonormal Gaussian process. Archive classification: math.PR math.FA math.MG Mathematics Subject Classification: Primary, 60D05, secondary, 60G15, 52A22 Remarks: 23 pages Submitted from: sachar.k at gmx.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.6113 or http://arXiv.org/abs/1404.6113

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sean Li From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:47:11 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Markov convexity and nonembeddability of the Heisenberg group" by Sean Li. Abstract: We compute the Markov convexity invariant of the continuous Heisenberg group $\mathbb{H}$ to show that it is Markov 4-convex and cannot be Markov $p$-convex for any $p < 4$. As Markov convexity is a biLipschitz invariant and Hilbert space is Markov 2-convex, this gives a different proof of the classical theorem of Pansu and Semmes that the Heisenberg group does not admit a biLipschitz embedding into any Euclidean space. The Markov convexity lower bound will follow from exhibiting an explicit embedding of Laakso graphs $G_n$ into $\mathbb{H}$ that has distortion at most $C n^{1/4} \sqrt{\log n}$. We use this to show that if $X$ is a Markov $p$-convex metric space, then balls of the discrete Heisenberg group $\mathbb{H}(\mathbb{Z})$ of radius $n$ embed into $X$ with distortion at least some constant multiple of $$\frac{(\log n)^{\frac{1}{p}-\frac{1}{4}}}{\sqrt{\log \log n}}.$$ Finally, we show somewhat unexpectedly that the optimal distortion of embeddings of binary trees $B_m$ into the infinite dimensional Heisenberg group is on the order of $\sqrt{\log m}$ Archive classification: math.MG math.FA Remarks: 20 pages Submitted from: seanli at math.uchicago.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.6751 or http://arXiv.org/abs/1404.6751

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Deping Ye From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:49:05 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory: Orlicz $\varphi$-radial addition, Orlicz $L_{\phi}$-dual mixed volume and related inequalities" by Deping Ye. Abstract: This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz $\varphi$-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz $\varphi$-radial addition of two star bodies, we derive a formula for the Orlicz $L_{\phi}$-dual mixed volume. Moreover, a dual Orlicz-Minkowski inequality for the Orlicz $L_{\phi}$-dual mixed volume, a dual Orlicz isoperimetric inequality for the Orlicz $L_{\phi}$-dual surface area and a dual Orlicz-Urysohn inequality for the Orlicz $L_{\phi}$-harmonic mean radius are proved. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A20, 53A15 Submitted from: deping.ye at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.6991 or http://arXiv.org/abs/1404.6991

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Narutaka Ozawa and Gilles Pisier From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:50:44 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A continuum of $\mathrm{C}^*$-norms on $\IB(H)\otimes \IB(H)$ and related tensor products" by Narutaka Ozawa and Gilles Pisier. Abstract: For any pair $M,N$ of von Neumann algebras such that the algebraic tensor product $M\otimes N$ admits more than one $\mathrm{C}^*$-norm, the cardinal of the set of $\mathrm{C}^*$-norms is at least $ {2^{\aleph_0}}$. Moreover there is a family with cardinality $ {2^{\aleph_0}}$ of injective tensor product functors for $\mathrm{C}^*$-algebras in Kirchberg's sense. Let $\IB=\prod_n M_{n}$. We also show that, for any non-nuclear von Neumann algebra $M\subset \IB(\ell_2)$, the set of $\mathrm{C}^*$-norms on $\IB \otimes M$ has cardinality equal to $2^{2^{\aleph_0}}$. Archive classification: math.OA Submitted from: pisier at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.7088 or http://arXiv.org/abs/1404.7088

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Stanislaw Kwapien, Mark Veraar, and Lutz Weis From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 2 May 2014 09:52:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "$R$-boundedness versus $\gamma$-boundedness" by Stanislaw Kwapien, Mark Veraar, and Lutz Weis. Abstract: It is well-known that in Banach spaces with finite cotype, the $R$-bounded and $\gamma$-bounded families of operators coincide. If in addition $X$ is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that $R$-boundedness implies $\gamma$-boundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that $R$-boundedness is stable under taking adjoints if and only if the underlying space is $K$-convex. Archive classification: math.FA math.PR Mathematics Subject Classification: 47B99 (Primary) 46B09, 46B07, 47B10 (Secondary) Submitted from: m.c.veraar at tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.7328 or http://arXiv.org/abs/1404.7328

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Karl-Mikael Perfekt From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:37:14 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Weak compactness of operators acting on o-O type spaces" by Karl-Mikael Perfekt. Abstract: We consider operators T : M_0 -> Z and T : M -> Z, where Z is a Banach space and (M_0, M) is a pair of Banach spaces belonging to a general construction in which M is defined by a "big-O" condition and M_0 is given by the corresponding "little-o" condition. The main result characterizes the weakly compact operators T in terms of a certain norm naturally attached to M, weaker than the M-norm. Further, we develop a method to extract c_0-subsequences from sequences in M_0. Applications are given to the characterizations of the weakly compact composition and Volterra-type integral operators on weighted spaces of analytic functions, BMOA, VMOA, and the Bloch space. Archive classification: math.FA math.CV Remarks: 12 pages Submitted from: karlmikp at math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0502 or http://arXiv.org/abs/1405.0502

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Alexander Koldobsky and Artem Zvavitch From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:38:41 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "An isomorphic version of the Busemann-Petty problem for arbitrary measures" by Alexander Koldobsky and Artem Zvavitch. Abstract: We prove the following theorem. Let $\mu$ be a measure on $R^n$ with even continuous density, and let $K,L$ be origin-symmetric convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any central hyperplane H. Then $\mu(K)\le \sqrt{n} \mu(L).$ We also prove this result with better constants for some special classes of measures and bodies. Finally, we prove a version of the hyperplane inequality for convex measures. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20 Submitted from: koldobskiya at missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0567 or http://arXiv.org/abs/1405.0567

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Alexander V. Kolesnikov and Emanuel Milman From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:40:25 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Remarks on the KLS conjecture and Hardy-type inequalities" by Alexander V. Kolesnikov and Emanuel Milman. Abstract: We generalize the classical Hardy and Faber-Krahn inequalities to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$, not necessarily vanishing on the boundary $\partial \Omega$. This reduces the study of the Neumann Poincar\'e constant on $\Omega$ to that of the cone and Lebesgue measures on $\partial \Omega$; these may be bounded via the curvature of $\partial \Omega$. A second reduction is obtained to the class of harmonic functions on $\Omega$. We also study the relation between the Poincar\'e constant of a log-concave measure $\mu$ and its associated K. Ball body $K_\mu$. In particular, we obtain a simple proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of $\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk. Archive classification: math.SP math.FA Remarks: 18 pages Submitted from: emanuel.milman at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0617 or http://arXiv.org/abs/1405.0617

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sergey Astashkin From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:41:48 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Disjointly homogeneous rearrangement invariant spaces via interpolation" by Sergey Astashkin. Abstract: A Banach lattice E is called p-disjointly homogeneous, 1< p< infty, when every sequence of pairwise disjoint normalized elements in E has a subsequence equivalent to the unit vector basis of l_p. Employing methods from interpolation theory, we clarify which rearrangement invariant (r.i.) spaces on [0,1] are p-disjointly homogeneous. In particular, for every 1<p< infty and any increasing concave function f on [0,1], which is not equivalent neither 1 nor t, there exists a p-disjointly homogeneous r.i. space with the fundamental function f. Moreover, in the class of all interpolation r.i. spaces with respect to the Banach couple of Lorentz and Marcinkiewicz spaces with the same fundamental function, dilation indices of which are non-trivial, for every 1<p< infty, there is only a unique p-disjointly homogeneous space. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B03, 46B70 Remarks: 23 pages Submitted from: astash at samsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0681 or http://arXiv.org/abs/1405.0681

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Deping Ye From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:43:14 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and geominimal surface areas" by Deping Ye. Abstract: This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which are dual to the Orlicz $L_{\phi}$ affine and geominimal surface areas for convex bodies (Ye, arXiv:1403.1643). These new affine invariants belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies (Ye, arXiv:1404.6991). Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequality, cyclic inequality, Santal\'{o} style inequality and Alexander-Fenchel type inequality are established. Besides, an Orlicz isoperimetric inequality for the Orlicz $\phi$-surface area and an Orlicz-Urysohn inequality for the Orlicz $\phi$ mean width are given. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A20, 53A15 Submitted from: deping.ye at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.0746 or http://arXiv.org/abs/1405.0746

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by N. Albuquerque, D. Nunez-Alarcon and D. M. Serrano-Rodríguez From: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:45:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A subexponential vector-valued Bohnenblust-Hille type inequality" by N. Albuquerque, D. Nunez-Alarcon and D. M. Serrano-Rodríguez. Abstract: Bayart, Pellegrino and Seoane recently proved that the polynomial Bohnenblust--Hille inequality for complex scalars is subexponential. We show that a vector valued polynomial Bohnenblust-Hille inequality on complex Banach lattices is also subexponential for some special cases. Our main result result recovers the best known constants of the classical polynomial inequality provided in \cite{bps}. Archive classification: math.FA Submitted from: ngalbqrq at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.1204 or http://arXiv.org/abs/1405.1204

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Grzegorz Plebanek and Damian Sobota m: alspach at math.okstate.edu (Dale Alspach) Date: Thu, 15 May 2014 14:47:32 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Countable tightness in the spaces of regular probability measures" by Grzegorz Plebanek and Damian Sobota. Abstract: We prove that if $K$ is a compact space and the space $P(K\times K)$ of regular probability measures on $K\times K$ has countable tightness in its $weak^*$ topology, then $L_1(\mu)$ is separable for every $\mu\in P(K)$. It has been known that such a result is a consequence of Martin's axiom MA$(\omega_1)$. Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todor\v{c}evi\'c on measures on Rosenthal compacta. Archive classification: math.FA Mathematics Subject Classification: Primary 46E15, 46E27, 54C35 Remarks: 9 pages Submitted from: grzes at math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.2527 or http://arXiv.org/abs/1405.2527

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Message concerning the death of Manuel Valdivia Date: Thu, 22 May 2014 08:42:41 -0500 To: banach at math.okstate.edu From: Dale Alspach <alspach at math.okstate.edu>

--------------------------------- Prof. Manuel Valdivia passed away April the 29th, 2014. He was member of the Spanish Academy of Sciences, professor at the Universitat de Valencia (Spain) and the Universidad Politecnica de Valencia (Spain), and Dr. Honoris Causa at various universities. Author of almost 200 research papers and several books in Functional Analysis, he was one of the outstanding mathematicians in Spain. Condolence messages may be sent to manuelvaldivia2014 at gmail.com Vicente Montesinos _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Third Announcement of BWB 2014 Date: Mon, 26 May 2014 18:20:09 -0300 To: banach at math.okstate.edu From: valentin ferenczi <ferenczi.math at gmail.com>

THIRD ANNOUNCEMENT OF BWB 2014 First Brazilian Workshop in Geometry of Banach Spaces August 25-29, 2014 Maresias, Sao Paulo State, Brazil. This is the third announcement for the First Brazilian Workshop in Geometry of Banach Spaces, organized by the University of Sao Paulo (USP), in the week August 25-29, 2014, at the Beach Hotel Maresias, on the coast of Sao Paulo State, in Maresias. We would like to recall that the ABSTRACT SUBMISSION deadline, MAY 31st, expires in a few days. Deadline for registration is June 30th. Please access the website of the conference: http://www.ime.usp.br/~banach/bwb2014/ Please CHECK the VISA SITUATION related to your travel document, as requirements for visa depend on bilateral relations between the two countries. For example, participants travelling with a US passport will need a visa. Please consult the website for all information and contact us at bwb2014 at gmail.com if you have any question. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) P. Dodos (U. Athens) G. Godefroy (Paris 6) W. B. Johnson (Texas A&M) P. Hayek (Czech Acad. & Cz. Polytech. U.) P. Koszmider (Polish Acad. Warsaw) C. Rosendal (U. Illinois Chicago) G. Schechtman (Weizmann Inst.) Th. Schlumprecht (Texas A&M) S. Todorcevic (CNRS Paris & U. Toronto) Scientific committee J. M. F. Castillo (U. Extremadura) V. Ferenczi (U. São Paulo, chair) R. Haydon (U. Oxford) W. B. Johnson (Texas A&M) G. Pisier (Paris 6 & Texas A&M) Th. Schlumprecht (Texas A&M) S. Todorcevic (CNRS Paris & U. Toronto) The organizers, F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Fall School ''Metric Embeddings: Constructions and Obstructions'' Date: Mon, 02 Jun 2014 20:26:43 -0000 To: "banach at www.math.okstate.edu" <banach at math.okstate.edu> From: BAUDIER Florent <florent.baudier at imj-prg.fr>

Dear Colleagues, We are looking for PhD students, postdocs or very young researchers that might be interested in being an active participant of the Fall School ''Metric Embeddings: Constructions and Obstructions'', that we will be organizing in Paris, 3-7 November 2014. The scientific committee will select 12 active participants from the pool of applicants. The deadline to apply is June 30, 2014. The description of the school, its organization and the application and selection processes are fully explained on the website of the Fall School. http://www.math.tamu.edu/~florent/fallschool.html The accommodation in Paris of an active participant will be fully taken care off and we should be able to partially (and eventually fully) cover its travel expenses. Feel free to spread the word to whom you think might be interested. Feel free also, to email us for additional information at florent.baudier at imj-p rg.fr The organizing committee, F. Baudier (Institut de Mathematiques de Jussieu-Paris Rive Gauche and Texas A&M University) G. Godefroy (Institut de Mathematiques de Jussieu-Paris Rive Gauche, CNRS) P. Pansu (Universite Paris-Sud 11) R. Tessera (Universite Paris-Sud 11, CNRS) _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Informal Analysis and Probability Seminar, October 17-19, 2014 Date: Wed, 11 Jun 2014 04:25:28 -0400 To: banach at math.okstate.edu From: zvavitch at math.kent.edu

Dear Colleague, Analysis/Probability group at the University of Michigan, and the Analysis group at Kent State University are happy to announce a meeting of the Informal Analysis and Probability Seminar, which will run at the Department of Mathematics at University of Michigan October 17-19, 2014. The plenary lecture series will be given by: Olivier Guedon (Pairs-Est University and University of Michigan), and Fedor Nazarov (Kent State) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local expenses, and possibly travel expenses, of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. Further information, and an online registration form, can be found online http://dept.math.lsa.umich.edu/conferences/informalAnalysis/. We encourage you to register as soon as possible, but to receive a support and/or help with hotel reservation, please, do register before September 5, 2014. Please feel free to contact us at rudelson at umich.edu / romanv at umich.edu for any further information. Sincerely, Analysis/Probability group at the University of Michigan, and the Analysis group at Kent State University _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by A. Jimenez-Vargas Date: Mon, 16 Jun 2014 13:13:13 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Weakly compact composition operators on spaces of Lipschitz functions" by A. Jimenez-Vargas. Abstract: Let $X$ be a pointed compact metric space. Assuming that $\mathrm{lip}_0(X)$ has the uniform separation property, we prove that every weakly compact composition operator on spaces of Lipschitz functions $\mathrm{Lip}_0(X)$ and $\mathrm{lip}_0(X)$ is compact. Archive classification: math.FA Mathematics Subject Classification: 47B33, 47B07, 26A16 Remarks: 6 pages Submitted from: ajimenez at ual.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4267 or http://arXiv.org/abs/1405.4267

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov Date: Mon, 16 Jun 2014 13:15:24 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Interpolation of nonlinear maps" by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov. Abstract: Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\subseteq X_0$ with norms satisfying $\|x\|_{X_0} \le c\|x\|_{X_1}$ for some $c > 0$. For any $0<\theta <1$, denote by $X_\theta = [X_0, X_1]_\theta$ and $Y_\theta = [Y_0, Y_1]_\theta$ the complex interpolation spaces and by $B(r, X_\theta)$, $0 \le \theta \le 1,$ the open ball of radius $r>0$ in $X_\theta$, centered at zero. Then for any analytic map $\Phi: B(r, X_0) \to Y_0+ Y_1$ such that $\Phi: B(r, X_0)\to Y_0$ and $\Phi: B(c^{-1}r, X_1)\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respectively, the restriction of $\Phi$ to $B(c^{-\theta}r, X_\theta)$, $0 < \theta < 1,$ is shown to be a map with values in $Y_\theta$ which is analytic and bounded by $M_0^{1-\theta} M_1^\theta$. Archive classification: math.FA Submitted from: p.topalov at neu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4253 or http://arXiv.org/abs/1405.4253

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by S Dutta and D Khurana Date: Mon, 16 Jun 2014 13:17:40 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Ordinal indices for complemented subspaces of l_p" by S Dutta and D Khurana. Abstract: We provide complete isomorphic invariance of a class of translation invariant complemented subspaces of L_p constructed by Bourgain, Rosenthal and Schechtman. We compute ordinal L_p-indices for this class. We further show that the isometric index of a tree subspace over a well founded tree is an invariance for the order of the tree. Finally we provide a dichotomy for the subspaces of L_p with small ordinal indices. Archive classification: math.FA Submitted from: divyakhurana11 at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.4499 or http://arXiv.org/abs/1405.4499

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Eusebio Gardella and Hannes Thiel Date: Mon, 16 Jun 2014 13:20:06 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Banach algebras generated by an invertible isometry of an $L^p$-space" by Eusebio Gardella and Hannes Thiel. Abstract: We study and classify Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. We associate to each such isometry a spectral invariant which contains considerably more information than its spectrum as an operator. We show that this invariant describes the isometric isomorphism type of the Banach algebra that the isometry generates together with its inverse. In the case of invertible isometries with full spectrum, these Banach algebras parametrize all completions of the group algebra $\mathbb{C}[\mathbb{Z}]$ corresponding to unital, contractive representations on $L^p$-spaces. The extreme cases are the algebra of $p$-pseudofunctions on $\mathbb{Z}$, and the commutative $C^*$-algebra $C(S^1)$. Moreover, there are uncountably many non-isometrically isomorphic "intermediate" algebras, all of which are shown to be closed under continuous functional calculus. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary: 46J40, 46H35. Secondary: 47L10 Remarks: 43 pages Submitted from: gardella at uoregon.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5589 or http://arXiv.org/abs/1405.5589

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg Date: Mon, 16 Jun 2014 13:21:34 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach) This is an announcement for the paper "Nigel Kalton and the interpolation theory of commutators" by Michael Cwikel, Mario Milman and Richard Rochberg.

Abstract: This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many topics in which Nigel made very significant and profound contributions deals with commutators in interpolation theory. It was our great privilege to work with him on one of his many papers about this topic. Our main purpose here is to offer} an introduction to that paper: A unified theory of commutator estimates for a class of interpolation methods. Adv. Math. 169 (2002), no. 2, 241--312. We sketch the theory of interpolation spaces constructed using pseudolattices which was developed in that paper and which enables quite general formulation of commutator theorems. We seek to place the results of that paper in the general context of preceding and subsequent research on this topic, also indicating some applications to other fields of analysis and possible directions for future research. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70, Secondary 42B20, 42B30, 46B42, 42B37, 35J60 Remarks: 16 pages 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/1405.5686 or http://arXiv.org/abs/1405.5686

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen Date: Mon, 16 Jun 2014 13:25:31 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Uniqueness of the maximal ideal of operators on the $\ell_p$-sum of $\ell_\infty^n\ (n\in\mathbb{N})$ for $1<p<\infty$" by Tomasz Kania and Niels Jakob Laustsen. Abstract: A recent result of Leung (Proceedings of the American Mathematical Society, to appear) states that the Banach algebra $\mathscr{B}(X)$ of bounded, linear operators on the Banach space $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_1}$ contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_p}$ and $X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_1^n\bigr)_{\ell_p}$ whenever $p\in(1,\infty)$. Archive classification: math.FA Submitted from: t.kania at lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5715 or http://arXiv.org/abs/1405.5715

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Will Grilliette Date: Mon, 16 Jun 2014 13:27:19 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Matricial Banach spaces" by Will Grilliette. Abstract: This work performs a study of the category of complete matrix-normed spaces, called matricial Banach spaces. Many of the usual constructions of Banach spaces extend in a natural way to matricial Banach spaces, including products, direct sums, and completions. Also, while the minimal matrix-norm on a Banach space is well-known, this work characterizes the maximal matrix-norm on a Banach space from the work of Effros and Ruan as a dual operator space. Moreover, building from the work of Blecher, Ruan, and Sinclair, the Haagerup tensor product is merged with the direct sum to form a Haagerup tensor algebra, which shares the analogous universal property of the Banach tensor algebra from the work of Leptin. Archive classification: math.FA Mathematics Subject Classification: 46M99 Remarks: 19 pages Submitted from: w.b.grilliette at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.5951 or http://arXiv.org/abs/1405.5951

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy Date: Mon, 16 Jun 2014 13:29:25 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces" by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy. Abstract: We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neither ``magic guesses'' nor calculations. Archive classification: math.CA math.DG math.FA Remarks: 11 pages Submitted from: dms at pdmi.ras.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.6229 or http://arXiv.org/abs/1405.6229

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Maria D. Acosta Date: Mon, 16 Jun 2014 13:30:55 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "The Bishop-Phelps-Bollob\'{a}s property for operators on $C(K)$" by Maria D. Acosta. Abstract: We provide a version for operators of the Bishop-Phelps-Bollob\'{a}s Theorem when the domain space is the complex space $C_0(L)$. In fact we prove that the space of weakly compact operators from the complex space $C_0(L)$ into a ${\mathbb C}$-uniformly convex space satisfies the Bishop-Phelps-Bollob\'{a}s property for operators. As a consequence, in the complex case, the space of operators from $C_0(L)$ into $L_p (\mu)$ ($1 \le p < \infty $) satisfies the Bishop-Phelps-Bollob\'{a}s property for operators. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B28, 47B99 Submitted from: dacosta at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.6428 or http://arXiv.org/abs/1405.6428

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Herve Queffelec, and Kristian Seip Date: Mon, 16 Jun 2014 13:33:06 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Approximation numbers of composition operators on $H^p$ spaces of Dirichlet series" by Herve Queffelec, and Kristian Seip. Abstract: By a theorem of Bayart, $\varphi$ generates a bounded composition operator on the Hardy space $\Hp$of Dirichlet series ($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is a nonnegative integer and $\psi$ a Dirichlet series with the following mapping properties: $\psi$ maps the right half-plane into the half-plane $\Real s >1/2$ if $c_0=0$ and is either identically zero or maps the right half-plane into itself if $c_0$ is positive. It is shown that the $n$th approximation numbers of bounded composition operators on $\Hp$ are bounded below by a constant times $r^n$ for some $0<r<1$ when $c_0=0$ and bounded below by a constant times $n^{-A}$ for some $A>0$ when $c_0$ is positive. Both results are best possible. Estimates rely on a combination of soft tools from Banach space theory ($s$-numbers, type and ecotype of Banach spaces, Weyl inequalities, and Schauder bases) and a certain interpolation method for $\Ht$, developed in an earlier paper, using estimates of solutions of the $\overline{\partial}$ equation. A transference principle from $H^p$ of the unit disc is discussed, leading to explicit examples of compact composition operators on $\Ho$ with approximation numbers decaying at a variety of sub-exponential rates. Archive classification: math.FA math.CV Submitted from: seip at math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.0445 or http://arXiv.org/abs/1406.0445

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Hana Bendova, Ondrej F.K. Kalenda and Jiri Spurny Date: Mon, 16 Jun 2014 13:35:24 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Quantification of the Banach-Saks property" by Hana Bendova, Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We further establish a quantitative version of the characterization of the weak Banach-Saks property of a set using uniform weak convergence and $\ell_1$-spreading models. We also study the case of the unit ball and in this case we prove a dichotomy which is an analogue of the James distortion theorem for $\ell_1$-spreading models. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 16 pages Submitted from: kalenda at karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.0684 or http://arXiv.org/abs/1406.0684

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikhail I. Ostrovskii Date: Mon, 16 Jun 2014 13:37:11 -0500 To: alspach at math.okstate.edu, banach at math.okstate.edu From: alspach at math.okstate.edu (Dale Alspach)

This is an announcement for the paper "Connections between metric characterizations of superreflexivity and Radon-Nikod\'ym property for dual Banach spaces" by Mikhail I. Ostrovskii. Abstract: Johnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon-Nikod\'ym property (RNP) for dual spaces in terms of the infinite diamond. This paper is devoted to further study of relations between metric characterizations of superreflexivity and the RNP for dual spaces. The main result is that finite subsets of any set $M$ whose embeddability characterizes the RNP for dual spaces, characterize superreflexivity. It is also observed that the converse statement does not hold, and that $M=\ell_2$ is a counterexample. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B85 (primary), 46B07, 46B22 (secondary) Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.0904 or http://arXiv.org/abs/1406.0904

Return-path: <alspach at math.okstate.edu> Subject: [Banach] School and conference 2nd announcement: Besancon, Autumn 2014 Date: Thu, 26 Jun 2014 18:37:50 +0200 To: banach at math.okstate.edu, gdr_afhp at listes.math.cnrs.fr From: Tony Prochazka <antonin.prochazka at univ-fcomte.fr>

Dear colleagues, This is the second annoncement of the two following closely related events. 1) The *Autum school on "Nonlinear geometry of Banach spaces and applications"*, in Metabief, France (October 20-24, 2014). The following mathematicians have kindly accepted our invitation to deliver a short course: Gilles Godefroy (Université Paris 6), Petr Hajek (Czech Academy of Sciences and Czech Technical University), Mikhail Ostrovskii (St. John's University, New York), Nirina Lovasoa Randrianarivony (Saint Louis University - to be confirmed), Guoliang Yu (Texas A&M University). Web: http://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=en Registration: Open until September 5. 2) The *conference on "Geometric functional analysis and its applications"* in Besancon, France (October 27-31, 2014). The following main speakers have already agreed to deliver a plenary lecture: Fernando Albiac (Univ. Publica de Navarra), Florent Baudier (Texas A&M University, Paris 6) , Robert Deville (Univ. Bordeaux) , Stephen Dilworth (Univ. South Carolina), Valentin Ferenczi (Univ. Sao Paulo) , Bill Johnson (Texas A&M University), Beata Randrianantoanina (Miami Univ Ohio), Gideon Schechtman (Weizmann Institute), Thomas Schlumprecht (Texas A&M University), Alain Valette (Univ. Neuchatel). Web: http://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=en Registration: Open until September 30. Participants will have the opportunity to give a short talk. The deadline for abstract submission is September 20. The purpose of these meetings is to bring together researchers and students with common interest in the field. They will offer many possibilities for informal discussions. Graduate students and others beginning their mathematical career are encouraged to participate. Thes two events are part of the trimester on "Geometric and noncommutative methods in functional analysis" organized by the "Laboratoire de Mathematiques de Besancon" during the Autumn 2014, see http://trimestres-lmb.univ-fcomte.fr/af.html . We are looking forward to meeting you! The organizers, Gilles Lancien and Tony Prochazka _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Amir Bahman Nasseri From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:16:51 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The spectrum of operators on C(K) with the Grothendieck Property and characterization of J-class operators which are adjoints" by Amir Bahman Nasseri. Abstract: This article deals with properties of spectra of operators on C(K)-spaces with the Grothendieck property (e.g. l^{\infty}) and application to so called J-class operators introduced by A. Manoussos and G. Costakis. We will show that C(K) has the Grothendieck property if and only if the boundary of the spectrum of every operator on C(K) consists entirely of eigenvalues of its adjoint. As a consequence we will see that there does not exist invertible J-class operators on C(K) with the Grothendieck property. In the third section we will give a quantitative and qualitative characterization of all J-class operators on l^{\infty} which are adjoints from operators on l^1. Archive classification: math.SP math.DS math.FA Remarks: 19 pages Submitted from: nasseri at uni-wuppertal.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.3815 or http://arXiv.org/abs/1406.3815

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:18:29 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A brief survey of Nigel Kalton's work on interpolation and related topics" by Michael Cwikel, Mario Milman and Richard Rochberg. Abstract: This is the third of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time, rather than concentrating on one particular paper, we attempt to give a general overview of Nigel's many contributions to the theory of interpolation of Banach spaces, and also, significantly, quasi-Banach spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70, 46A16. Secondary 42B20, 42B30 Remarks: 11 pages 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/1406.3842 or http://arXiv.org/abs/1406.3842

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by S. Astashkin, F. Sukochev, and D. Zanin From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:20:12 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p" by S. Astashkin, F. Sukochev, and D. Zanin. Abstract: Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B20, 46B09 Remarks: 14 pages, submitted Submitted from: astash at samsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.4950 or http://arXiv.org/abs/1406.4950

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Khalil Saadi From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:29:57 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Some properties for Lipschitz strongly p-summing operators" by Khalil Saadi. Abstract: We consider the space of molecules endowed with the transpose version of the Chevet-Saphar norm and we identify its dual space with the space of Lipschitz strongly p-summing operators. We also extend some old results to the category of Lipschitz mappings and we give a factorization result of Lipschitz (p,r,s)-summing operators. Archive classification: math.FA Mathematics Subject Classification: [2000] 47B10, 46B28, 47L20 Remarks: 19 pages Submitted from: kh_saadi at yahoo.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.5551 or http://arXiv.org/abs/1406.5551

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:37:25 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Tukey classification of some ideals in $\omega$ and the lattices of weakly compact sets in Banach spaces" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez. Abstract: We study the lattice structure of the family of weakly compact subsets of the unit ball $B_X$ of a separable Banach space $X$, equipped with the inclusion relation (this structure is denoted by $\mathcal{K}(B_X)$) and also with the parametrized family of almost inclusion relations $K \subseteq L+\epsilon B_X$, where $\epsilon>0$ (this structure is denoted by $\mathcal{AK}(B_X)$). Tukey equivalence between partially ordered sets and a suitable extension to deal with $\mathcal{AK}(B_X)$ are used. Assuming the axiom of analytic determinacy, we prove that separable Banach spaces fall into four categories, namely: $\mathcal{K}(B_X)$ is equivalent either to a singleton, or to $\omega^\omega$, or to the family $\mathcal{K}(\mathbb{Q})$ of compact subsets of the rational numbers, or to the family $[\mathfrak{c}]^{<\omega}$ of all finite subsets of the continuum. Also under the axiom of analytic determinacy, a similar classification of $\mathcal{AK}(B_X)$ is obtained. For separable Banach spaces not containing $\ell^1$, we prove in ZFC that $\mathcal{K}(B_X) \sim \mathcal{AK}(B_X)$ are equivalent to either $\{0\}$, $\omega^\omega$, $\mathcal{K}(\mathbb{Q})$ or $[\mathfrak{c}]^{<\omega}$. The lattice structure of the family of all weakly null subsequences of an unconditional basis is also studied. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B20(Primary), 03E60, 03E75, 06A06, 46B50, 03E75 Submitted from: avileslo at um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.5526 or http://arXiv.org/abs/1406.5526

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Javier Alejandro Chavez-Dominguez From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:39:31 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Lipschitz $p$-convex and $q$-concave maps" by Javier Alejandro Chavez-Dominguez. Abstract: The notions of $p$-convexity and $q$-concavity are mostly known because of their importance as a tool in the study of isomorphic properties of Banach lattices, but they also play a role in several results involving linear maps between Banach spaces and Banach lattices. In this paper we introduce Lipschitz versions of these concepts, dealing with maps between metric spaces and Banach lattices, and start by proving nonlinear versions of two well-known factorization theorems through $L_p$ spaces due to Maurey/Nikishin and Krivine. We also show that a Lipschitz map from a metric space into a Banach lattice is Lipschitz $p$-convex if and only if its linearization is $p$-convex. Furthermore, we elucidate why there is such a close relationship between the linear and nonlinear concepts by proving characterizations of Lipschitz $p$-convex and Lipschitz $q$-concave maps in terms of factorizations through $p$-convex and $q$-concave Banach lattices, respectively, in the spirit of the work of Raynaud and Tradacete. Archive classification: math.FA Remarks: 25 pages Submitted from: jachavezd at math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6357 or http://arXiv.org/abs/1406.6357

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Javier Alejandro Chavez-Dominguez and Denka Kutzarova From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:42:04 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Stability of low-rank matrix recovery and its connections to Banach space geometry" by Javier Alejandro Chavez-Dominguez and Denka Kutzarova. Abstract: There are well-known relationships between compressed sensing and the geometry of the finite-dimensional $\ell_p$ spaces. A result of Kashin and Temlyakov can be described as a characterization of the stability of the recovery of sparse vectors via $\ell_1$-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional $\ell_1$ and $\ell_2$ spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich proves an analogous relationship even for $\ell_p$ spaces with $p < 1$. In this paper we prove what we call matrix or noncommutative versions of these results: we characterize the stability of low-rank matrix recovery via Schatten $p$-(quasi-)norm minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional Schatten $p$-spaces. Archive classification: math.FA cs.IT math.IT Remarks: 19 pages, 1 figure Submitted from: jachavezd at math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6712 or http://arXiv.org/abs/1406.6712

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Felix Cabello Sanchez, Jesus M. F. Castillo and Nigel J. Kalton From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:44:27 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Complex interpolation and twisted twisted Hilbert spaces" by Felix Cabello Sanchez, Jesus M. F. Castillo and Nigel J. Kalton. Abstract: We show that Rochberg's generalizared interpolation spaces $\mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to \mathscr Z^{(k)} \to 0$. We study some structural properties of those sequences; in particular, we show that nontriviality, having strictly singular quotient map, or having strictly cosingular embedding depend only on the basic case $n=k=1$. If we focus on the case of Hilbert spaces obtained from the interpolation scale of $\ell_p$ spaces, then $\mathscr Z^{(2)}$ becomes the well-known Kalton-Peck $Z_2$ space; we then show that $\mathscr Z^{(n)}$ is (or embeds in, or is a quotient of) a twisted Hilbert space only if $n=1,2$, which solves a problem posed by David Yost; and that it does not contain $\ell_2$ complemented unless $n=1$. We construct another nontrivial twisted sum of $Z_2$ with itself that contains $\ell_2$ complemented. Archive classification: math.FA Mathematics Subject Classification: 46M18, 46B70, 46B20 Submitted from: castillo at unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6723 or http://arXiv.org/abs/1406.6723

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jesus M. F. Castillo, Manuel Gonzalez and Pier Luigi Papini From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:46:08 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On nested sequences of convex sets in a Banach space" by Jesus M. F. Castillo, Manuel Gonzalez and Pier Luigi Papini. Abstract: In this paper we study different aspects of the representation of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach space $X$ via a nested sequence of closed convex bounded sets of $X$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: This paper is to appear in Studia Mathematica Submitted from: castillo at unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6725 or http://arXiv.org/abs/1406.6725

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 30 Jun 2014 13:47:50 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "$\aleph$-injective Banach spaces and $\aleph$-projective compacta" by Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno. Abstract: A Banach space $E$ is said to be injective if for every Banach space $X$ and every subspace $Y$ of $X$ every operator $t:Y\to E$ has an extension $T:X\to E$. We say that $E$ is $\aleph$-injective (respectively, universally $\aleph$-injective) if the preceding condition holds for Banach spaces $X$ (respectively $Y$) with density less than a given uncountable cardinal $\aleph$. We perform a study of $\aleph$-injective and universally $\aleph$-injective Banach spaces which extends the basic case where $\aleph=\aleph_1$ is the first uncountable cardinal. When dealing with the corresponding ``isometric'' properties we arrive to our main examples: ultraproducts and spaces of type $C(K)$. We prove that ultraproducts built on countably incomplete $\aleph$-good ultrafilters are $(1,\aleph)$-injective as long as they are Lindenstrauss spaces. We characterize $(1,\aleph)$-injective $C(K)$ spaces as those in which the compact $K$ is an $F_\aleph$-space (disjoint open subsets which are the union of less than $\aleph$ many closed sets have disjoint closures) and we uncover some projectiveness properties of $F_\aleph$-spaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 54B30, 46B08, 54C15, 46B26 Remarks: This paper is to appear in Revista Matem\'atica Iberoamericana Submitted from: castillo at unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6733 or http://arXiv.org/abs/1406.6733

Return-path: <alspach at math.okstate.edu> Subject: [Banach] SUMIRFAS 2014 Date: Wed, 02 Jul 2014 15:02:32 -0500 To: banach at math.okstate.edu From: Bill Johnson <johnson at math.tamu.edu>

1st ANNOUNCEMENT OF SUMIRFAS 2014 The Summer Informal Regional Functional Analysis Seminar July 25-27 Texas A&M University, College Station The speakers for SUMIRFAS 2014 are March Boedihardjo Gilles Pisier Michael Brannan Lova Randrianarivony Caleb Eckhardt Dan Voiculescu Matthew Kennedy Deping Ye Vern Paulsen The schedule for SUMIRFAS will be posted on the Workshop in Analysis and Probability webpage: http://www.math.tamu.edu/~kerr/workshop 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 166. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html Coffee and refreshments will be available in Blocker 148. SUMIRFAS will be preceded by a Concentration Week on Free Probability from July 21 to 25. Topics will include operator algebras, the connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The webpage is located at: http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 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>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. For information about the Concentration Week on Free Probability contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema <ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu>. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] SUMIRFAS 2014 From: Bill Johnson <johnson at math.tamu.edu> Date: Mon, 21 Jul 2014 12:32:44 -0500 (CDT) To: banach at math.okstate.edu

2nd ANNOUNCEMENT OF SUMIRFAS 2014 The Summer Informal Regional Functional Analysis Seminar July 25-27 Texas A&M University, College Station The speakers for SUMIRFAS 2014 are March Boedihardjo A new characterization of certain quasidiagonal operators Michael Brannan L_p -representations of discrete quantum groups and exotic quantum group C*-algebras Caleb Eckhardt Unitary representations of nilpotent groups and the structure of the C*-algebras they generate Matthew Kennedy Boundaries of reduced C*-algebras of discrete groups Vern Paulsen Quantum chromatic numbers Gilles Pisier A continuum of C*-norms on B(H)?B(H) and related tensor products Lova Randrianarivony TBA Dan Voiculsecu Some C*-algebras which are coronas of non-C*-Banach algebras Deping Ye Is Einstein's "spooky action" common? The webpage for SUMIRFAS, including links to the schedule and abstracts, can be found at http://www.math.tamu.edu/~kerr/workshop/sumirfas2014 The first talk will be at 2:00 pm on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 166. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html SUMIRFAS will be preceded by a Concentration Week on Free Probability from July 21 to 25. Topics will include operator algebras, the connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The webpage is located at: http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 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>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. For information about the Concentration Week on Free Probability contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema <ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu>. _______________________________________________ Banach mailing list Banach at www.math.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Said Amana Abdillah, Jean Esterle, andBernhard Hermann Haak From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 12:53:40 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Sur quelques extensions au cadre Banachique de la notion d'op\'erateur de Hilbert-Schmidt" by Said Amana Abdillah, Jean Esterle, and Bernhard Hermann Haak. Abstract: In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing operators, $\gamma$-summing or $\gamma$-radonifying operators, weakly $*1$-nuclear operators and classes of operators defined via factorization properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt operators as the class of all operators $u:E\to F$ such that $w\circ u \circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\to E$ and every bounded operator $w:F\to H_2$, where $H_1$ et $H_2$ are Hilbert spaces. Besides the trivial case where one of the spaces $E$ or $F$ is a "Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces $E$ or $F$ is a Hilbert space. Archive classification: math.FA Remarks: 18 pages Submitted from: bernhard.haak at math.u-bordeaux1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.7546 or http://arXiv.org/abs/1406.7546

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Slawomir Borzdynski and Andrzej Wisnicki From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 12:56:49 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings" by Slawomir Borzdynski and Andrzej Wisnicki. Abstract: It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty nonexpansive retract of $C$. This partially solves a long-standing open problem in metric fixed point theory in the case of commutative semigroups. Archive classification: math.FA Submitted from: awisnic at hektor.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.0359 or http://arXiv.org/abs/1407.0359

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Stephan Fackler From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 12:58:50 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Regularity properties of sectorial operators: counterexamples and open problems" by Stephan Fackler. Abstract: We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples. Archive classification: math.FA Mathematics Subject Classification: 47D06 (Primary) 47A60, 35K90 (Secondary) Remarks: 21 pages Submitted from: stephan.fackler at uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.1142 or http://arXiv.org/abs/1407.1142

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kallol Paul, Puja Ghosh, and Debmalya Sain From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:01:11 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On rectangular constant in normed linear spaces" by Kallol Paul, Puja Ghosh, and Debmalya Sain. Abstract: We study the properties of rectangular constant $ \mu(\mathbb{X}) $ in a normed linear space $\mathbb{X}$. We prove that $ \mu(\mathbb{X}) = 3$ iff the unit sphere contains a straight line segment of length 2. In fact, we prove that the rectangular modulus attains its upper bound iff the unit sphere contains a straight line segment of length 2. We prove that if the dimension of the space $\mathbb{X}$ is finite then $\mu(\mathbb{X})$ is attained. We also prove that a normed linear space is an inner product space iff we have sup$\{\frac{1+|t|}{\|y+tx\|}$: $x,y \in S_{\mathbb{X}}$ with $x\bot_By\} \leq \sqrt{2}$ $\forall t$ satisfying $|t|\in (3-2\sqrt{2},\sqrt{2}+1)$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 47A30 Submitted from: kalloldada at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.1353 or http://arXiv.org/abs/1407.1353

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sergo A. Episkoposian From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:02:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "$L^1$- convergence of greedy algorithm by generalized Walsh system" by Sergo A. Episkoposian. Abstract: In this paper we consider the generalized Walsh system and a problem $L^1- convergence$ of greedy algorithm of functions after changing the values on small set. Archive classification: math.FA Mathematics Subject Classification: 42A65, 42A20 Submitted from: sergoep at ysu.am The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.1496 or http://arXiv.org/abs/1407.1496

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Miek Messerschmidt From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:45:24 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Geometric duality theory of cones in dual pairs of vector spaces" by Miek Messerschmidt. Abstract: This paper will generalize what may be termed the ``geometric duality theory'' of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual Banach space. We show that geometric duality theory is not restricted to real pre-ordered Banach spaces, as is done classically, but can naturally extended to real Banach spaces endowed with arbitrary collections of closed cones. We define geometric notions of normality, conormality, additivity and coadditivity for members of dual pairs of real vector spaces as certain possible interactions between two cones and two convex convex sets containing zero. We show that, thus defined, these notions are dual to each other under certain conditions, i.e., for a dual pair of real vector spaces $(Y,Z)$, the space $Y$ is normal (additive) if and only if its dual $Z$ is conormal (coadditive) and vice versa. These results are set up in a manner so as to provide a framework to prove results in the geometric duality theory of cones in real Banach spaces. As an example of using this framework, we generalize classical duality results for real Banach spaces pre-ordered by a single closed cone, to real Banach spaces endowed with an arbitrary collections of closed cones. As an application, we analyze some of the geometric properties of naturally occurring cones in C*-algebras and their duals. Archive classification: math.FA Mathematics Subject Classification: Primary: 46A20, Secondary: 46B10, 46B20, 46A40, 46B40, 46L05 Submitted from: mmesserschmidt at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.2434 or http://arXiv.org/abs/1407.2434

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Riku Klen, Antti Rasila, and Jarno Talponen From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:48:57 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On smoothness of quasihyperbolic balls" by Riku Klen, Antti Rasila, and Jarno Talponen. Abstract: We investigate properties of quasihyperbolic balls and geodesics in Euclidean and Banach spaces. Our main result is that in uniformly smooth Banach spaces a quasihyperbolic ball of a convex domain is $C^1$-smooth. The question about the smoothness of quasihyperbolic balls is old, originating back to the discussions of F.W. Gehring and M. Vuorinen in 1970's. To our belief, the result is new also in the Euclidean setting. We also address some other issues involving the smoothness of quasihyperbolic balls. We introduce an interesting application of quasihyperbolic metrics to renormings of Banach spaces. To provide a useful tool for this approach we turn our attention to the variational stability of quasihyperbolic geodesics. Several examples and illustrations are provided. Archive classification: math.FA math.CV Mathematics Subject Classification: 30C65, 46T05, 46B03 Remarks: 19 pages, 4 figures Submitted from: antti.rasila at iki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.2403 or http://arXiv.org/abs/1407.2403

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Ioannis Gasparis From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:50:16 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "An extension of James's compactness theorem" by Ioannis Gasparis. Abstract: Let X and Y be Banach spaces and F a subset of B_{Y^*}. Endow Y with the topology \tau_F of pointwise convergence on F. Let T: X^* \to Y be a bounded linear operator which is (w^*, \tau_F) continuous. Assume that every vector in the range of T attains its norm at an element of F. Then it is proved that T is (w^*,w) continuous. Archive classification: math.FA Mathematics Subject Classification: 46 Remarks: 15 pages Submitted from: ioagaspa at math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.3655 or http://arXiv.org/abs/1407.3655

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Vladimir Kadets, Miguel Martin, Javier Meri, and Dirk Werner From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:51:45 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Lipschitz slices and the Daugavet equation for Lipschitz operators" by Vladimir Kadets, Miguel Martin, Javier Meri, and Dirk Werner. Abstract: We introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer to the non-linear case some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators. Archive classification: math.FA Mathematics Subject Classification: Primary 46B04. Secondary 46B80, 46B22, 47A12 Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.4018 or http://arXiv.org/abs/1407.4018

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Peter G. Casazza From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:53:27 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Consequences of the Marcus/Spielman/Stivastava solution to the Kadison-Singer Problem" by Peter G. Casazza. Abstract: It is known that the famous, intractible 1959 Kadison-Singer problem in $C^{*}$-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. The recent surprising solution to this problem by Marcus, Spielman and Srivastava was a significant achievement and a significant advance for all these areas of research. We will look at many of the known equivalent forms of the Kadison-Singer Problem and see what are the best new theorems available in each area of research as a consequence of the work of Marcus, Spielman and Srivastave. In the cases where {\it constants} are important for the theorem, we will give the best constants available in terms of a {\it generic constant} taken from \cite{MSS}. Thus, if better constants eventually become available, it will be simple to adapt these new constants to the theorems. Archive classification: math.FA Mathematics Subject Classification: 42A05, 42A10, 42A16, 43A50, 46B03, 46B07, 46L05, Submitted from: casazzap at missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.4768 or http://arXiv.org/abs/1407.4768

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kallol Paul, Debmalya Sain and Lokenath Debnath From: alspach at math.okstate.edu (Dale Alspach) Date: Mon, 21 Jul 2014 13:55:15 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A conjecture on the characterisation of inner product spaces" by Kallol Paul, Debmalya Sain and Lokenath Debnath. Abstract: We study the properties of strongly orthonormal Hamel basis in the sense of Birkhoff-James in a finite dimensional real normed linear space that are analogous to the properties of orthonormal basis in an inner product space. We relate the notion of strongly orthonormal Hamel basis in the sense of Birkhoff-James with the notions of best approximation and best coapproximation in a finite dimensional real normed linear space. We prove that the existence of best coapproximation to any element of the normed linear space out of any one dimensional subspace and its coincidence with the best approximation to that element out of that subspace characterises a real inner product space of dimension( > 2). Finally we conjecture that a finite dimensional real smooth normed space of dimension ($>2$) is an inner product space iff given any element on the unit sphere there exists a strongly orthonormal Hamel basis in the sense of Birkhoff-James containing that element. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B20, Secondary: 47A30 Submitted from: kalloldada at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.5016 or http://arXiv.org/abs/1407.5016

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Iian B. Smythe From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:09:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Borel equivalence relations in the space of bounded operators" by Iian B. Smythe. Abstract: We consider various notions of equivalence in the space of bounded operators on a Hilbert space, including modulo finite rank operators, modulo Schatten $p$-classes, and modulo compact operators. Using Hjorth's theory of turbulence, the latter two are shown to be not classifiable by countable structures, while the first cannot be reduced to the orbit equivalence relation of any Polish group action. The results for modulo finite rank and modulo compact operators are also shown for the restrictions of these equivalence relations to the space of projection operators. Families of non-classifiable equivalence relations on sequence spaces are described and utilized in these results. Archive classification: math.LO math.OA Mathematics Subject Classification: Primary 03E15, 47B10, Secondary 47C15, 46A45 Remarks: 36 pages Submitted from: ibs24 at cornell.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.5325 or http://arXiv.org/abs/1407.5325

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Ben Wallis From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:11:11 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Constructing Banach ideals using upper $\ell_p$-estimates" by Ben Wallis. Abstract: Using upper $\ell_p$-estimates for normalized weakly null sequence images, we describe a new family of operator ideals $\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$ and $1\leq\xi\leq\omega_1$. These classes contain the completely continuous operators, and are distinct for all choices $1\leq p\leq\infty$ and, when $p\neq 1$, for all choices $\xi\neq\omega_1$. For the case $\xi=1$, there exists an ideal norm $\|\cdot\|_{(p,1)}$ on the class $\mathcal{WD}_{\ell_p}^{(\infty,1)}$ under which it forms a Banach ideal. Archive classification: math.FA Mathematics Subject Classification: 47L20, 46B45, 46A45, 46B25 Submitted from: wallis at math.niu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.5948 or http://arXiv.org/abs/1407.5948

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:12:51 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Octahedral norms in spaces of operators" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda Zoca. Abstract: We study octahedral norms in the space of bounded linear operators between Banach spaces. In fact, we prove that $L(X,Y)$ has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a consequence the space of operators $L(\ell_1 ,X)$ has octahedral norm if, and only if, $X$ has octahedral norm. These results also allows us to get the stability of strong diameter 2 property for projective tensor products of Banach spaces, which is an improvement of the known results about the size of nonempty relatively weakly open subsets in the unit ball of the projective tensor product of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: 16 pages Submitted from: glopezp at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.6038 or http://arXiv.org/abs/1407.6038

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by A. Jimenez-Vargas, J.M. Sepulcre, and Moises Villegas-Vallecillos From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:14:53 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Biduality and density in Lipschitz function spaces" by A. Jimenez-Vargas, J.M. Sepulcre, and Moises Villegas-Vallecillos. Abstract: For pointed compact metric spaces $(X,d)$, we address the biduality problem as to when the space of Lipschitz functions $\mathrm{Lip}_0(X,d)$ is isometrically isomorphic to the bidual of the space of little Lipschitz functions $\mathrm{lip}_0(X,d)$, and show that this is the case whenever the closed unit ball of $\mathrm{lip}_0(X,d)$ is dense in the closed unit ball of $\mathrm{Lip}_0(X,d)$ with respect to the topology of pointwise convergence. Then we apply our density criterion to prove in an alternate way the real version of a classical result which asserts that $\mathrm{Lip}_0(X,d^\alpha)$ is isometrically isomorphic to $\mathrm{lip}_0(X,d^\alpha)^{**}$ for any $\alpha$ in $(0,1)$. Archive classification: math.FA Mathematics Subject Classification: 46E10, 46E15, 46J10 Remarks: 7 pages Submitted from: ajimenez at ual.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.7599 or http://arXiv.org/abs/1407.7599

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee and Miguel Martin From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:16:29 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On Banach spaces with the approximate hyperplane series property" by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee and Miguel Martin. Abstract: We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollob\'{a}s version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of $w^*$-continuous operators and other related results. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Remarks: 12 pages Submitted from: hanjulee at dongguk.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.7848 or http://arXiv.org/abs/1407.7848

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sun Kwang Kim and Han Ju Lee From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:17:57 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The Bishop-Phelps-Bollob\'as property for operators from $\mathcal{C}(K)$ to uniformly convex spaces" by Sun Kwang Kim and Han Ju Lee. Abstract: We show that the pair $(C(K),X)$ has the Bishop-Phelps-Bolloba\'as property for operators if $K$ is a compact Hausdorff space and $X$ is a uniformly convex space. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Citation: To apprear in J. Math. Anal. Appl. 2014 Remarks: 7 pages Submitted from: hanjulee at dongguk.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.7872 or http://arXiv.org/abs/1407.7872

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Yanni Chen From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:19:30 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Lebesgue and Hardy spaces for symmetric norms I" by Yanni Chen. Abstract: In this paper, we define and study a class $\mathcal{R}_{c}$ of norms on $L^{\infty}\left( \mathbb{T}\right) $, called $continuous\ rotationally\ symmetric \ norms$, which properly contains the class $\left \{ \left \Vert \cdot \right \Vert _{p}:1\leq p<\infty \right \} .$ For $\alpha \in \mathcal{R}% _{c}$ we define $L^{\alpha}\left( \mathbb{T}\right) $ and the Hardy space $H^{\alpha}\left( \mathbb{T}\right) $, and we extend many of the classical results, including the dominated convergence theorem, convolution theorems, dual spaces, Beurling-type invariant spaces, inner-outer factorizations, characterizing the multipliers and the closed densely-defined operators commuting with multiplication by $z$. We also prove a duality theorem for a version of $L^{\alpha}$ in the setting of von Neumann algebras. Archive classification: math.OA Submitted from: yet2 at wildcats.unh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.7920 or http://arXiv.org/abs/1407.7920

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Pavlos Motakis, Daniele Puglisi and Despoina Zisimopoulou From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:21:45 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A hierarchy of separable commutative Calkin algebras" by Pavlos Motakis, Daniele Puglisi and Despoina Zisimopoulou. Abstract: For specific well founded countably branching trees $\mathcal{T}$ we construct $\mathcal{L}_\infty$ spaces $X_{\mathcal{T}}$. For each such tree $\mathcal{T}$ the Calkin algebra of $X_{\mathcal{T}}$ strongly resembles $C(\mathcal{T})$, the algebra of continuous functions defined on $\mathcal{T}$ and in the case in which $\mathcal{T}$ has finite height, those two algebras are homomorphic. We conclude that for every countable compact metric space $K$ with finite Cantor-Bendixson index there exists a $\mathcal{L}_\infty$ space whose Calkin algebra is isomorphic, as a Banach algebra, to $C(K)$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B25, 46B28 Remarks: 28 pages Submitted from: pmotakis at central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.8073 or http://arXiv.org/abs/1407.8073

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Antonin Prochazka and Luis Sanchez-Gonzalez From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:23:35 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Low distortion embeddings between $C(K)$ spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez. Abstract: We show that, for each ordinal $\alpha<\omega_1$, the space $C([0,\omega^\alpha])$ does not embed into $C(K)$ with distortion strictly less than $2$ unless $K^{(\alpha)}\neq \emptyset$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B85 Remarks: 11 pages Submitted from: antonin.prochazka at univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.0211 or http://arXiv.org/abs/1408.0211

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kevin Beanland, Daniel Freeman and Pavlos Motakis From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:25:40 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The stabilized set of $p$'s in Krivine's theorem can be disconnected" by Kevin Beanland, Daniel Freeman and Pavlos Motakis. Abstract: For any closed subset $F$ of $[1,\infty]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space $X$ with a 1-unconditional basis is constructed so that in each block subspace $Y$ of $X$, $\ell_p$ is finitely block represented in $Y$ if and only if $p \in F$. In particular, this solves the question as to whether the stabilized Krivine set for a Banach space had to be connected. We also prove that for every infinite dimensional subspace $Y$ of $X$ there is a dense subset $G$ of $F$ such that the spreading models admitted by $Y$ are exactly the $\ell_p$ for $p\in G$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B06, 46B07, 46B25, 46B45 Remarks: 25 pages Submitted from: pmotakis at central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.0265 or http://arXiv.org/abs/1408.0265

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by J. Lopez-Abad and P. Tradacete From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:27:05 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Bases of random unconditional convergence in Banach spaces" by J. Lopez-Abad and P. Tradacete. Abstract: We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases and existence of unconditional subsequences. Archive classification: math.FA Mathematics Subject Classification: 46B09, 46B15 Submitted from: ptradace at math.uc3m.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.0478 or http://arXiv.org/abs/1408.0478

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman and Tomasz Tkocz From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 8 Aug 2014 13:28:48 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Injective Tauberian operators on $L_1$ and operators with dense range on $\ell_\infty$" by William B. Johnson, Amir Bahman Nasseri, Gideon Schechtman and Tomasz Tkocz. Abstract: There exist injective Tauberian operators on $L_1(0,1)$ that have dense, non closed range. This gives injective, non surjective operators on $\ell_\infty$ that have dense range. Consequently, there are two quasi-complementary, non complementary subspaces of $\ell_\infty$ that are isometric to $\ell_\infty$. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B08, 47A53 Submitted from: gideon at weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.1443 or http://arXiv.org/abs/1408.1443

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by M. G. Cabrera-Padilla, J. A. Chavez-Dominguez, A. Jimenez-Vargas, and Moises Villegas-Vallecillos From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:05:10 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Lipschitz tensor product" by M. G. Cabrera-Padilla, J. A. Chavez-Dominguez, A. Jimenez-Vargas, and Moises Villegas-Vallecillos. Abstract: Inspired by ideas of R. Schatten in his celebrated monograph on a theory of cross-spaces, we introduce the notion of a Lipschitz tensor product X\boxtimes E of a pointed metric space and a Banach space E as a certain linear subspace of the algebraic dual of Lipo(X,E^*). We prove that <Lipo(X,E^*),X\boxtimes E> forms a dual pair. We prove that X\boxtimes E is linearly isomorphic to the linear space of all finite-rank continuous linear operators from (X^#,T) into E, where X^# denotes the space Lipo(X,K) and T is the topology of pointwise convergence of X^#. The concept of Lipschitz tensor product of elements of X^# and E^* yields the space X^#\boxast E^* as a certain linear subspace of the algebraic dual of X\boxtimes E. To ensure the good behavior of a norm on X\boxtimes E with respect to the Lipschitz tensor product of Lipschitz functionals (mappings) and bounded linear functionals (operators), the concept of dualizable (respectively, uniform) Lipschitz cross-norm on X\boxtimes E is defined. We show that the Lipschitz injective norm epsilon, the Lipschitz projective norm pi and the Lipschitz p-nuclear norm d_p (1<=p<=infty) are uniform dualizable Lipschitz cross-norms on X\boxtimes E. In fact, epsilon is the least dualizable Lipschitz cross-norm and pi is the greatest Lipschitz cross-norm on X\boxtimes E. Moreover, dualizable Lipschitz cross-norms alpha on X\boxtimes E are characterized by satisfying the relation epsilon<=alpha<=pi. In addition, the Lipschitz injective (projective) norm on X\boxtimes E can be identified with the injective (respectively, projective) tensor norm on the Banach-space tensor product between the Lipschitz-free space over X and E. In terms of the space X^#\boxast E^*, we describe the spaces of Lipschitz compact (finite-rank, approximable) operators from X to E^$. Archive classification: math.FA Mathematics Subject Classification: 26A16, 46B28, 46E15, 47L20 Remarks: 31 pages Submitted from: ajimenez at ual.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.1874 or http://arXiv.org/abs/1408.1874

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Enrique A. Sanchez-Perez From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:07:42 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The product duality formula in Banach space theory" by Enrique A. Sanchez-Perez. Abstract: In this paper we analyze a definition of product of Banach spaces that is naturally associated by duality with an abstract notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of the functional analysis, that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown. Archive classification: math.FA Mathematics Subject Classification: 46A32, 46E30, 47A30, 46B10 Remarks: 14 pages Submitted from: easancpe at mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.2147 or http://arXiv.org/abs/1408.2147

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Thomas Schlumprecht From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:09:32 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On Zippin's embedding theorem of Banach spaces into Banach spaces with bases" by Thomas Schlumprecht. Abstract: We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach space with a separable dual embeds into one with a shrinking basis. This new proof leads to improved versions of other embedding results. Archive classification: math.FA Mathematics Subject Classification: 46B03 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/1408.3311 or http://arXiv.org/abs/1408.3311

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Amit Maji and P. D. Srivastava From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:17:28 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On some geometric properties of generalized Musielak-Orlicz sequence space and corresponding operator ideals" by Amit Maji and P. D. Srivastava. Abstract: Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$ be a real Banach space and $A$ be any infinite matrix. In this paper, a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold {\Phi}}^{A}(X)$ is introduced. It is shown that the space is complete normed linear space under certain conditions on the matrix $A$. It is also shown that $l_{\bold{\Phi}}^{A}(X)$ is a $\sigma$- Dedikind complete whenever $X$ is so. We have discussed some geometric properties, namely, uniformly monotone, uniform Opial property for this space. Using the sequence of $s$-number (in the sense of Pietsch), the operators of $s$-type $l_{\bold{\Phi}}^{A}$ and operator ideals under certain conditions on the matrix $A$ are discussed. Archive classification: math.FA Mathematics Subject Classification: 46A45, 47B06, 47L20 Remarks: 18 pages Submitted from: amaji at maths.iitkgp.ernet.in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.3528 or http://arXiv.org/abs/1408.3528

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Eusebio Gardella and Martino Lupini From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:19:58 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Representations of \'{e}tale groupoids on $L^p$-spaces" by Eusebio Gardella and Martino Lupini. Abstract: For $p\in (1,\infty)$, we study representations of \'{e}tale groupoids on $L^{p}$-spaces. Our main result is a generalization of Renault's disintegration theorem for representations of \'{e}tale groupoids on Hilbert spaces. We establish a correspondence between $L^{p}$-representations of an \'{e}tale groupoid $G$, contractive $L^{p}$-representations of $C_{c}(G)$, and tight regular $L^{p}$-representations of any countable inverse semigroup of open slices of $G$ that is a basis for the topology of $G$. We define analogs $F^{p}(G)$ and $F_{\mathrm{red}}^{p}(G)$ of the full and reduced groupoid C*-algebras using representations on $L^{p}$-spaces. As a consequence of our main result, we deduce that every contractive representation of $F^{p}(G)$ or $F_{\mathrm{red}}^{p}(G)$ is automatically completely contractive. Examples of our construction include the following natural families of Banach algebras: discrete group $L^{p}$-operator algebras, the analogs of Cuntz algebras on $L^{p}$-spaces, and the analogs of AF-algebras on $L^{p} $-spaces. Our results yield new information about these objects: their matricially normed structure is uniquely determined. More generally, groupoid $L^{p}$-operator algebras provide analogs of several families of classical C*-algebras, such as Cuntz-Krieger C*-algebras, tiling C*-algebras, and graph C*-algebras. Archive classification: math.OA Mathematics Subject Classification: 47L10, 22A22 (Primary) 46H05 (Secondary) Remarks: 52 pages Submitted from: mlupini at yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.3752 or http://arXiv.org/abs/1408.3752

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by H. Garth Dales From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:21:47 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Maximal ideals in commutative Banach algebras" by H. Garth Dales. Abstract: We show that each maximal ideal in a commutative Banach algebra has codimension 1. Archive classification: math.FA math.RA Submitted from: t.kania at lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.3815 or http://arXiv.org/abs/1408.3815

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava, From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:23:51 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Ramanujan graphs and the solution of the Kadison-Singer problem" by Adam W. Marcus, Daniel A. Spielman, and Nikhil Srivastava,. Abstract: We survey the techniques used in our recent resolution of the Kadison-Singer problem and proof of existence of Ramanujan Graphs of every degree: mixed characteristic polynomials and the method of interlacing families of polynomials. To demonstrate the method of interlacing families of polynomials, we give a simple proof of Bourgain and Tzafriri's restricted invertibility principle in the isotropic case. Archive classification: math.SP math.CO math.OA Mathematics Subject Classification: 05C50, 46L05, 26C10 Remarks: A version of this paper will appear in the proceedings of the 2014 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.4421 or http://arXiv.org/abs/1408.4421

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Yong Jiao, Anming Yang, Lian Wu, and Rui Yi From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:27:04 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The predual and John-Nirenberg inequalities on generalized BMO martingale spaces" by Yong Jiao, Anming Yang, Lian Wu, and Rui Yi. Abstract: In this paper we introduce the generalized BMO martingale spaces by stopping time sequences, which enable us to characterize the dual spaces of martingale Hardy-Lorentz spaces $H_{p,q}^s$ for $0<p\leq1, 1<q<\infty$. Moreover, by duality we obtain a John-Nirenberg theorem for the generalized BMO martingale spaces when the stochastic basis is regular. We also extend the boundedness of fractional integrals to martingale Hardy-Lorentz spaces. Archive classification: math.FA Mathematics Subject Classification: 60G46, 60G42 Remarks: 23pages Submitted from: jiaoyong at csu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.4641 or http://arXiv.org/abs/1408.4641

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Dario Trevisan From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:28:22 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "A short proof of Stein's universal multiplier theorem" by Dario Trevisan. Abstract: We give a short proof of Stein's universal multiplier theorem, purely by probabilistic methods, thus avoiding any use of harmonic analysis techniques (complex interpolation or transference methods). Archive classification: math.FA Submitted from: dario.trevisan at sns.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.4752 or http://arXiv.org/abs/1408.4752

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kevin Beanland, Ryan Causey, and Pavlos Motakis From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 22 Aug 2014 10:30:05 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Arbitrarily distortable Banach spaces of higher order" by Kevin Beanland, Ryan Causey, and Pavlos Motakis. Abstract: We study an ordinal rank on the class of Banach spaces with bases that quantifies the distortion of the norm of a given Banach space. The rank $AD(\cdot)$, introduced by P. Dodos, uses the transfinite Schreier familes and has the property that $AD(X) < \omega_1$ if and only if $X$ is arbitrarily distortable. We prove several properties of this rank as well as some new results concerning higher order $\ell_1$ spreading models. We also compute this rank for for several Banach spaces. In particular, it is shown that class of Banach spaces $\mathfrak{X}^{\omega^\xi}_{0,1}$ , which each admit $\ell_1$ and $c_0$ spreading models hereditarily, and were introduced by S.A. Argyros, the first and third author, satisfy $AD(\mathfrak{X}^{\omega^\xi}_{0,1}) = \omega^\xi + 1$. This answers some questions of Dodos. Archive classification: math.FA Submitted from: CAUSEYRM at mailbox.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.5065 or http://arXiv.org/abs/1408.5065

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Assaf Naor and Gideon Schechtman From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 12:56:13 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Metric ${X}_p$ inequalities" by Assaf Naor and Gideon Schechtman. Abstract: We show that if $m,n\in \mathbb{N}$ and $k\in \{1,\ldots, n\}$ satisfy $m\ge \frac{n^{3/2}}{\sqrt{k}}$ then for every $p\in [2,\infty)$ and $f:\mathbb{Z}_{4m}^n\to \mathbb{R}$ we have \begin{equation} \frac{1}{\binom{n}{k}}\sum_{\substack{S\subseteq \{1,\ldots,n\}\\|S|= k}}\frac{\mathbb{E}\left[\big|f\big(x+2m\sum_{j\in S} \varepsilon_j e_j\big)-f(x)\big|^p\right]}{m^p}\lesssim_p \frac{k}{n}\sum_{j=1}^n\mathbb{E}\big[\left| f(x+e_j)-f(x)\right|^p\big]+\left(\frac{k}{n}\right)^{\frac{p}{2}} \mathbb{E}\big[\left|f\left(x+ \varepsilon{e}\right)-f(x)\right|^p\big], \end{equation} where the expectation is with respect to $(x,\varepsilon)\in \mathbb{Z}_{4m}^n\times \{-1,1\}^n$ chosen uniformly at random and $e_1,\ldots e_n$ is the standard basis of $\mathbb{Z}_{4m}^n$. The above inequality is a nonlinear extension of a linear inequality for Rademacher sums that was proved by Johnson, Maurey, Schechtman and Tzafriri in 1979. We show that for the above statement to hold true it is necessary that $m$ tends to infinity with $n$. The formulation (and proof) of the above inequality completes the long-standing search for bi-Lipschitz invariants that serve as an obstruction to the nonembeddability of $L_p$ spaces into each other, the previously understood cases of which were metric notions of type and cotype, which fail to certify the nonembeddability of $L_q$ into $L_p$ when $2<q<p$. Among the consequences of the above inequality are new quantitative restrictions on the bi-Lipschitz embeddability into $L_p$ of snowflakes of $L_q$ and integer grids in $\ell_q^n$, for $2<q<p$. As a byproduct of our investigations, we also obtain results on the geometry of the Schatten $p$ trace class $S_p$ that are new even in the linear setting. Archive classification: math.FA math.MG math.OA 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/1408.5819 or http://arXiv.org/abs/1408.5819

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Afonso S. Bandeira and Ramon van Handel From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 12:57:51 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Sharp nonasymptotic bounds on the norm of random matrices with independent entries" by Afonso S. Bandeira and Ramon van Handel. Abstract: We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If $X$ is the $n\times n$ symmetric matrix with $X_{ij}\sim N(0,b_{ij}^2)$, we show that $$\mathbf{E}\|X\|\lesssim \max_i\sqrt{\sum_{j}b_{ij}^2} +\max_{ij}|b_{ij}|\sqrt{\log n}. $$ This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general subgaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm. The proofs are based on a combination of the moment method and geometric functional analysis techniques. As an application, we show that our bounds immediately yield the correct phase transition behavior of the spectral edge of random band matrices and of sparse Wigner matrices. We also recover a result of Seginer on the norm of Rademacher matrices. Archive classification: math.PR math.FA Mathematics Subject Classification: 60B20, 46B09, 60F10 Remarks: 23 pages Submitted from: rvan at princeton.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.6185 or http://arXiv.org/abs/1408.6185

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by S. J. Dilworth, Denka Kutzarova, and N. Lovasoa Randrianarivony From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 12:59:31 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The transfer of property $(\beta)$ of Rolewicz by a uniform quotient" by S. J. Dilworth, Denka Kutzarova, and N. Lovasoa Randrianarivony. Abstract: We provide a Laakso construction to prove that the property of having an equivalent norm with the property $(\beta)$ of Rolewicz is qualitatively preserved via surjective uniform quotient mappings between separable Banach spaces. On the other hand, we show that the $(\beta)$-modulus is not quantitatively preserved via such a map by exhibiting two uniformly homeomorphic Banach spaces that do not have $(\beta)$-moduli of the same power-type even under renorming. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20 (Primary), 46B80, 46T99, 51F99 (Secondary) Submitted from: nrandria at slu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.6424 or http://arXiv.org/abs/1408.6424

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Carlos H. Jimenez and Ignacio Villanueva From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:01:15 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Characterization of dual mixed volumes via polymeasures" by Carlos H. Jimenez and Ignacio Villanueva. Abstract: We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we reprove, with these same techniques, a recently found characterization of the dual mixed volume. Archive classification: math.FA Submitted from: ignaciov at mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.6796 or http://arXiv.org/abs/1408.6796

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by I. Asekritova, N. Kruglyak and M. Mastylo From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:02:50 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Interpolation of Fredholm operators" by I. Asekritova, N. Kruglyak and M. Mastylo. Abstract: We prove novel results on interpolation of Fredholm operators including an abstract factorization theorem. The main result of this paper provides sufficient conditions on the parameters $\theta \in (0,1)$ and $q\in \lbrack 1,\infty ]$ under which an operator $A$ is a Fredholm operator from the real interpolation space $(X_{0},X_{1})_{\theta ,q}$ to $(Y_{0},Y_{1})_{\theta ,q} $ for a given operator $A\colon (X_{0},X_{1})\rightarrow (Y_{0},Y_{1})$ between compatible pairs of Banach spaces such that its restrictions to the endpoint spaces are Fredholm operators. These conditions are expressed in terms of the corresponding indices generated by the $K$-functional of elements from the kernel of the operator $A$ in the interpolation sum $X_{0}+X_{1}$. If in addition $q\in \lbrack 1,\infty )$ and $A$ is invertible operator on endpoint spaces, then these conditions are also necessary. We apply these results to obtain and present an affirmative solution of the famous Lions-Magenes problem on the real interpolation of closed subspaces. We also discuss some applications to the spectral theory of operators as well as to perturbation of the Hardy operator by identity on weighted $L_{p}$-spaces. Archive classification: math.FA Submitted from: mastylo at amu.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1408.7024 or http://arXiv.org/abs/1408.7024

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Olav Nygaard From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:04:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Uniform boundedness deciding sets, and a problem of M. Valdivia" by Olav Nygaard. Abstract: We prove that if a set $B$ in a Banach space $X$ can be written as an increasing, countable union $B=\cup_n B_n$ of sets $B_n$ such that no $B_n$ is uniform boundedness deciding, then also $B$ is not uniform boundedness deciding. From this we can give a positive answer to a question of M. Valdivia. Archive classification: math.FA Remarks: 5 pages Submitted from: olav.nygaard at uia.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.0102 or http://arXiv.org/abs/1409.0102

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Valentin Ferenczi and Christian Rosendal From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:06:22 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Non-unitarisable representations and maximal symmetry" by Valentin Ferenczi and Christian Rosendal. Abstract: We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique invariant complemented subspace. This is subsequently combined with rigidity results for the unitary representation of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite regular tree, to describe the possible bounded subgroups of ${\rm GL}(\mathcal H)$ extending a well-known non-unitarisable representation of $\mathbb F_\infty$. As a related result, we also show that a transitive norm on a separable Banach space must be strictly convex. Archive classification: math.FA Submitted from: rosendal.math at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.0141 or http://arXiv.org/abs/1409.0141

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Oleg Reinov From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:11:24 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "O-frames for operators in Banach spaces" by Oleg Reinov. Abstract: These notes are formal. Here, in this abstract, not in the note, we should say that all that is in the text was done, essentially, by Aleksander Pe{\l}czy\'nski. BUT: Anyhow, a new notion of an O-frame for an operator is introduced. For the operators in separable spaces, it is shown that a operator has an O-frame iff it has the BAP iff it can be factored through a Banach space with a basis. Applications are given. However, looking around, I'd say that, e.g., a notion of a Banach frame (and also O-frame) was implicitely introduced by great Aleksander Pe{\l}czy\'nski. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 11 pages, was as a SPb Math. Soc. preprint, in RUSSIAN! Submitted from: orein51 at mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.0165 or http://arXiv.org/abs/1409.0165

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by S Dutta and D Khurana From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 13:14:35 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Ordinal indices of small subspaces of $L_p$" by S Dutta and D Khurana. Abstract: We calculate ordinal $L_p$ index defined in "An ordinal L_p index for Banach spaces with an application to complemented subspaces of L_p" authored by J. Bourgain, H. P. Rosenthal and G. Schechtman, for Rosenthal's space $X_p$, $\ell_p$ and $\ell_2$. We show a subspace of $L_p$ $(2 < p < \infty)$ non isomorphic to $\ell_2$ embeds in $\ell_p$ if and only if its ordinal index is minimum possible. We also give a sufficient condition for a $\mathcal{L}_p$ subspace of $\ell_p\oplus\ell_2$ to be isomorphic to $X_p$. Archive classification: math.FA Submitted from: divyakhurana11 at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.2330 or http://arXiv.org/abs/1409.2330

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Dong Hoon Cho and Yun Sung Choi From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 14:34:39 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Bishop-Phelps-Bolloba's theorem on bounded closed convex sets" by Dong Hoon Cho and Yun Sung Choi. Abstract: This paper deals with the \emph{Bishop-Phelps-Bollob\'as property} (\emph{BPBp} for short) on bounded closed convex subsets of a Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove that the \emph{BPBp} holds for bounded linear functionals on arbitrary bounded closed convex subsets of a real Banach space. We show that for all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also that for a Banach space $Y$ with property $(\beta )$ the pair $(X,Y)$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of an arbitrary Banach space $X$. For a bounded closed absorbing convex subset $D$ of $X$ with positive modulus convexity we get that the pair $(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further obtain that for an Asplund space $X$ and for a locally compact Hausdorff $L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed absolutely convex subset $D$ of $X$. Finally we study the stability of the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or $\ell_{\infty}$-sum of a family of Banach spaces. Archive classification: math.FA Submitted from: meimi200 at postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.3008 or http://arXiv.org/abs/1409.3008

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Thomas Schlumprecht and Andras Zsak From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 12 Sep 2014 14:35:59 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The algebra of bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals" by Thomas Schlumprecht and Andras Zsak. Abstract: We prove that in the reflexive range $1<p<q<\infty$ the algebra of all bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals. This solves a problem raised by A. Pietsch in his book `Operator ideals'. Archive classification: math.FA Mathematics Subject Classification: 47L20, 46B25 Remarks: 18 pages Submitted from: a.zsak at dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.3480 or http://arXiv.org/abs/1409.3480

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Dimosthenis Drivaliaris and Nikos Yannakakis From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 26 Sep 2014 12:48:42 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "The angle of an operator and range and kernel complementarity" by Dimosthenis Drivaliaris and Nikos Yannakakis. Abstract: We show that if the angle of a bounded linear operator on a Banach space with closed range is less than $\pi$, then its range and kernel are complementary. We also show that in finite dimensions and up to rotations this simple geometric property characterizes operators for which range and kernel are complementary. For operators on a Hilbert space we present a sufficient condition, involving the distance of the boundary of the numerical range from the origin, for the range and the kernel to be complementary. Archive classification: math.FA Mathematics Subject Classification: 47A05, 47A12, 47A10, 47B44, 46B20 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/1409.4195 or http://arXiv.org/abs/1409.4195

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Fernanda Botelho From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 26 Sep 2014 12:50:47 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Isometries and Hermitian operators on Zygmund spaces" by Fernanda Botelho. Abstract: In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho at memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5378 or http://arXiv.org/abs/1409.5378

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Fernanda Botelho and James Jamison From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 26 Sep 2014 12:52:27 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "Isometries and Hermitian operators on $\mathcal{B}_0(\triangle, E)$" by Fernanda Botelho and James Jamison. Abstract: In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho at memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5381 or http://arXiv.org/abs/1409.5381

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kati Ain and Eve Oja From: alspach at math.okstate.edu (Dale Alspach) Date: Fri, 26 Sep 2014 12:57:36 -0500 (CDT) To: alspach at math.okstate.edu, banach at math.okstate.edu

This is an announcement for the paper "On $(p,r)$-null sequences and their relatives" by Kati Ain and Eve Oja. Abstract: Let $1\leq p < \infty$ and $1\leq r \leq p^\ast$, where $p^\ast$ is the conjugate index of $p$. We prove an omnibus theorem, which provides numerous equivalences for a sequence $(x_n)$ in a Banach space $X$ to be a $(p,r)$-null sequence. One of them is that $(x_n)$ is $(p,r)$-null if and only if $(x_n)$ is null and relatively $(p,r)$-compact. This equivalence is known in the ''limit'' case when $r=p^\ast$, the case of the $p$-null sequence and $p$-compactness. Our approach is more direct and easier than those applied for the proof of the latter result. We apply it also to characterize the unconditional and weak versions of $(p,r)$-null sequences. Archive classification: math.FA Submitted from: kati.ain at ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.6476 or http://arXiv.org/abs/1409.6476

Return-path: <alspach at math.okstate.edu> Subject: Announcement of a special issue of Annals of Functional Analysis From: Dale Alspach <alspach at math.okstate.edu> Date: Sun, Oct 12, 2014 at 3:56 PM To: banach at mathdept.okstate.edu

Dear Colleague, I would like to inform you that a special issue (2016) of the Annals of Functional Analysis (AFA) is dedicated to Professor Anthony To-Ming Lau for his significant contributions to several areas of Functional Analysis, Abstract Harmonic Analysis and Operator Theory. The journal particularly invites articles related to works of A. T.-M. Lau, but other papers within the scope of the journal (MSC43, MSC46 and MSC47) are warmly welcomed. The usual reviewing procedures and standards of AFA will be applied to all papers for the special issue. Preliminary papers or summaries of results previously published are not acceptable. %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Submission should be done via the online submission of AFA at: http://www.emis.de/journals/AFA/ The deadline for submission is: *** 30 March 2015 *** %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Please let the editor-in-chief know whether you are potentially able to have a contribution to this issue or not (and give an approximate date for receiving your paper, if possible). Best wishes, M. S. Moslehian Editor-in-chief http://www.um.ac.ir/~moslehian/

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Niels Jakob Laustsen and Richard Skillicorn From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:38:27 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Splittings of extensions of the algebra of bounded operators on a space" by Niels Jakob Laustsen and Richard Skillicorn. Abstract: We show that there exist a Banach space E, a unital Banach algebra A with Jacobson radical rad A, and a continuous, surjective algebra homomorphism f from A onto the Banach algebra B(E) of bounded operators on E such that ker f = rad A and the corresponding extension {0} -> rad A -> A -> B(E) -> {0} is singular (in the sense that rad A has trivial multiplication) and splits algebraically, but it does not split strongly. This conclusion complements the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999). The Banach space E that we use is a quotient of the l_2-direct sum of an infinite sequence of James-type quasi-reflexive Banach spaces; it was originally introduced by Read (J. London Math. Soc. 1989). Archive classification: math.FA Submitted from: r.skillicorn at lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.8203 or http://arXiv.org/abs/1409.8203

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Demuth, Franz Hanauska, Marcel Hansmann, and Guy Katriel From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:40:22 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Estimating the number of eigenvalues of linear operators on Banach spaces" by Michael Demuth, Franz Hanauska, Marcel Hansmann, and Guy Katriel. Abstract: Let $L_0$ be a bounded operator on a Banach space, and consider a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned with obtaining bounds on the number of eigenvalues of $L$ in subsets of the complement of the essential spectrum of $L_0$, in terms of the approximation numbers of the perturbing operator $K$. Our results can be considered as wide generalizations of classical results on the distribution of eigenvalues of compact operators, which correspond to the case $L_0=0$. They also extend previous results on operators in Hilbert space. Our method employs complex analysis and a new finite-dimensional reduction, allowing us to avoid using the existing theory of determinants in Banach spaces, which would require strong restrictions on $K$. Several open questions regarding the sharpness of our results are raised, and an example is constructed showing that there are some essential differences in the possible distribution of eigenvalues of operators in general Banach spaces, compared to the Hilbert space case. Archive classification: math.SP math.FA Submitted from: marcel.hansmann at mathematik.tu-chemnitz.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.8569 or http://arXiv.org/abs/1409.8569

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mark Rudelson From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:42:18 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "On the complexity of the set of unconditional convex bodies" by Mark Rudelson. Abstract: We show that for any t>1, the set of unconditional convex bodies in R^n contains a t-separated subset of cardinality at least 0.1 exp exp (C(t) n). This implies that there exists an unconditional convex body in R^n which cannot be approximated within the distance d by a projection of a polytope with N faces unless N > exp(c(d)n). We also show that for t>2, the cardinality of a t-separated set of completely symmetric bodies in R^n does not exceed exp exp (c(t)(log n)^2). Archive classification: math.MG math.FA Remarks: 17 pages Submitted from: rudelson at umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.0092 or http://arXiv.org/abs/1410.0092

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Sun Kwang Kim, Han Ju Lee, and Miguel Martin From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:43:59 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Bishop-Phelps-Bollob\'as property for bilinear forms on spaces of continuous functions" by Sun Kwang Kim, Han Ju Lee, and Miguel Martin. Abstract: It is shown that the Bishop-Phelps-Bollob\'as theorem holds for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary locally compact topological Hausdorff spaces $L_1$ and $L_2$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.0514 or http://arXiv.org/abs/1410.0514

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jochen Gl\"uck From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:46:19 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Spectral and asymptotic properties of contractive semigroups on non-Hilbert spaces" by Jochen Gl\"uck. Abstract: We analyse $C_0$-semigroups of contractive operators on real-valued $L^p$-spaces for $p \not= 2$ and on other classes of non-Hilbert spaces. We show that, under some regularity assumptions on the semigroup, the geometry of the unit ball of those spaces forces the semigroup's generator to have only trivial (point) spectrum on the imaginary axis. This has interesting consequences for the asymptotic behaviour as $t \to \infty$. For example, we can show that a contractive and eventually norm continuous $C_0$-semigroup on a real-valued $L^p$-space automatically converges strongly if $p \not\in \{1,2,\infty\}$. Archive classification: math.FA Mathematics Subject Classification: 47D06 Remarks: 26 pages Submitted from: jochen.glueck at uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.2502 or http://arXiv.org/abs/1410.2502

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by David Alonso-Gutierrez, Bernardo Gonzalez, C. Hugo Jimenez, and Rafael Villa From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:48:31 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Rogers-Shephard inequality for log-concave functions" by David Alonso-Gutierrez, Bernardo Gonzalez, C. Hugo Jimenez, and Rafael Villa. Abstract: In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary 52A20, Secondary 39B62, 46N10 Remarks: 24 pages Submitted from: carloshugo at us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.2556 or http://arXiv.org/abs/1410.2556

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Martino Lupini From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:50:10 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Uniqueness, universality, and homogeneity of the noncommutative Gurarij space" by Martino Lupini. Abstract: We realize the noncommutative Gurarij space $\mathbb{NG}$ defined by Oikhberg as the Fra\"{\i}ss\'{e} limit of the class of finite-dimensional $1$-exact operator spaces. As a consequence we deduce that the noncommutative Gurarij space is unique up to completely isometric isomorphism, homogeneous, and universal among separable $1$-exact operator spaces. Moreover we show that $\mathbb{NG}$ is isometrically isomorphic to the Gurarij Banach space. Therefore $\mathbb{NG}$ can be thought as a canonical operator space structure on the Gurarij Banach space. Archive classification: math.FA math.LO Mathematics Subject Classification: 46L07 (Primary) 03C30 (Secondary) Remarks: 24 pages Submitted from: mlupini at yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.3345 or http://arXiv.org/abs/1410.3345

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:52:29 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Subspaces of Banach spaces with big slices" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda. Abstract: We study when diameter two properties pass down to subspaces. We obtain that the slice two property (respectively diameter two property, strong diameter two property) passes down from a Banach space $X$ to a subspace $Y$ whenever $Y$ is complemented by a norm one projection with finite-dimensional kernel (respectively the quotient $X/Y$ is finite dimensional, $X/Y$ is strongly regular). Also we study the same problem for dual properties of the above ones, as having octahedral, weakly octahedral or 2-rough norm. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: 12 pages Submitted from: glopezp at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4324 or http://arXiv.org/abs/1410.4324

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:55:30 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Diameter two properties in James spaces" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda. Abstract: We study the diameter two properties in the spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane $M$ of $JH_\infty$ whose topological dual space enjoys the $w^*$-strong diameter two property and also $M$ and $M^*$ have an octahedral norm. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Remarks: 19 pages Submitted from: glopezp at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4325 or http://arXiv.org/abs/1410.4325

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Cwikel and Richard Rochberg From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:56:56 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Nigel Kalton and complex interpolation of compact operators" by Michael Cwikel and Richard Rochberg. Abstract: This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time we discuss Nigel's partial solutions (obtained jointly with one of us) of the problem of whether the complex method of interpolation preserves the compactness of operators. This problem is now 51 years old and still lacks a complete solution. We also survey some other partial solutions of this problem, obtained before and after the above mentioned joint work. We plan a technical sequel to this paper, which may contain some small new results and will probably conclude this series devoted to Nigel's research. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70 Remarks: 12 pages 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/1410.4527 or http://arXiv.org/abs/1410.4527

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Julio Delgado, Michael Ruzhansky and Baoxiang Wang From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 13:58:41 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Approximation property and nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces" by Julio Delgado, Michael Ruzhansky and Baoxiang Wang. Abstract: In this paper we first prove the metric approximation property for weighted mixed-norm Lebesgue spaces. Then, using Gabor frame representation we show that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck's theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these space as well as derive the corresponding trace formulae. Finally, we apply the notion of nuclearity to functions of the harmonic oscillator on modulation spaces. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary 46B26, 47B38, Secondary 47G10, 47B06, 42B35 Remarks: 20 pages Submitted from: m.ruzhansky at imperial.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4687 or http://arXiv.org/abs/1410.4687

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 14:00:34 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Banach lattice versions of strict singularity" by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete. Abstract: We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span of any disjoint sequence, coincides with that of lattice strictly singular operators, i.e. those not invertible on any (infinite dimensional) sublattice. New results are given which help to clarify the existing relation between these two classes. Archive classification: math.FA Mathematics Subject Classification: 46B42, 47B60 Submitted from: ptradace at math.uc3m.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4752 or http://arXiv.org/abs/1410.4752

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jarno Talponen From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 21 Oct 2014 14:01:57 -0500 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Note on order-isomorphic isometric embeddings of some recent function spaces" by Jarno Talponen. Abstract: We investigate certain recently introduced ODE-determined varying exponent $L^p$ spaces. It turns out that these spaces are finitely representable in a concrete universal varying exponent $\ell^p$ space. Moreover, this can be accomplished in a natural unified fashion. This leads to order-isomorphic isometric embeddings of all of the above $L^p$ spaces to an ultrapower of the above varying exponent $\ell^p$ space. Archive classification: math.FA math.CA Mathematics Subject Classification: 46E30, 46B08, 46B04, 46B42, 46B45, 34-XX Submitted from: talponen at iki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.4961 or http://arXiv.org/abs/1410.4961

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jesus M. F. Castillo, Valentin Ferenczi and Manuel Gonzalez From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 14:52:24 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Singular twisted sums generated by complex interpolation" by Jesus M. F. Castillo, Valentin Ferenczi and Manuel Gonzalez. Abstract: We present new methods to obtain singular twisted sums $X\oplus_\Omega X$ (i.e., exact sequences $0\to X\to X\oplus_\Omega X \to X\to 0$ in which the quotient map is strictly singular), in which $X$ is the interpolation space arising from a complex interpolation scheme and $\Omega$ is the induced centralizer. Although our methods are quite general, in our applications we are mainly concerned with the choice of $X$ as either a Hilbert space, or Ferenczi's uniformly convex Hereditarily Indecomposable space. In the first case, we construct new singular twisted Hilbert spaces, including the only known example so far: the Kalton-Peck space $Z_2$. In the second case we obtain the first example of an H.I. twisted sum of an H.I. space. We then use Rochberg's description of iterated twisted sums to show that there is a sequence $\mathcal F_n$ of H.I. spaces so that $\mathcal F_{m+n}$ is a singular twisted sum of $\mathcal F_m$ and $\mathcal F_n$, while for $l>n$ the direct sum $\mathcal F_n \oplus \mathcal F_{l+m}$ is a nontrivial twisted sum of $\mathcal F_l$ and $\mathcal F_{m+n}$. We also introduce and study the notion of disjoint singular twisted sum of K\"othe function spaces and construct several examples involving reflexive $p$-convex K\"othe function spaces, which include the function version of the Kalton-Peck space $Z_2$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B70, 46M18 Submitted from: castillo at unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5505 or http://arXiv.org/abs/1410.5505

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mario Chica, Vladimir Kadets, Miguel Martin, Javier Meri, and Soloviova From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 14:53:57 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Two refinements of the Bishop-Phelps-Bollob\'as modulus" by Mario Chica, Vladimir Kadets, Miguel Martin, Javier Meri, and Soloviova. Abstract: Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\'as proved the nowadays known as the Bishop-Phelps-Bollob\'as theorem, which allows to approximate at the same time a functional and a vector in which it almost attains the norm. Very recently, two Bishop-Phelps-Bollob\'as moduli of a Banach space have been introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\'as theorem in this space. In this paper we present two refinements of the results of that paper. On the one hand, we get a sharp general estimation of the Bishop-Phelps-Bollob\'as modulus as a function of the norms of the point and the functional, and we also calculate it in some examples, including Hilbert spaces. On the other hand, we relate the modulus of uniform non-squareness with the Bishop-Phelps-Bollob\'as modulus obtaining, in particular, a simpler and quantitative proof of the fact that a uniformly non-square Banach space cannot have the maximum value of the Bishop-Phelps-Bollob\'as modulus. Archive classification: math.FA Mathematics Subject Classification: 46B04 Submitted from: mmartins at ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5570 or http://arXiv.org/abs/1410.5570

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Silvia Lassalle and Pablo Turco From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 14:55:34 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "The weak bounded approximation property for $\mathcal A$" by Silvia Lassalle and Pablo Turco. Abstract: Fixed a Banach operator ideal $\mathcal A$, we introduce and investigate the weak bounded approximation property for $\mathcal A$, which is strictly weaker than the bounded approximation property for $\mathcal A$ of Lima, Lima and Oja (2010). We relate the weak BAP for $\mathcal A$ with approximation properties given by tensor norms and show that the metric approximation property of order $p$ of Saphar is the weak BAP for the ideal of $p'$-summing operators, $1<p<\infty$, $\frac 1p + \frac 1{p'}=1$. Under this framework, we address the question of approximation properties passing from $X'$ to $X$ or from $X''$ to $X'$. Archive classification: math.FA Mathematics Subject Classification: 47B10, 46A32, 46B28 Remarks: 15 Pages Submitted from: paturco at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5670 or http://arXiv.org/abs/1410.5670

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Pandelis Dodos, Vassilis Kanellopoulos and Konstantinos Tyros From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 15:16:52 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "A concentration inequality for product spaces" by Pandelis Dodos, Vassilis Kanellopoulos and Konstantinos Tyros. Abstract: We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior. Archive classification: math.PR math.CO math.FA Remarks: 11 pages, no figures Submitted from: pdodos at math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5965 or http://arXiv.org/abs/1410.5965

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Pandelis Dodos, Vassilis Kanellopoulos and Thodoris Karageorgos From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 15:18:22 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Szemer\'{e}di's regularity lemma via martingales" by Pandelis Dodos, Vassilis Kanellopoulos and Thodoris Karageorgos. Abstract: We prove a variant of the abstract probabilistic version of Szemer\'{e}di's regularity lemma, due to Tao, which applies to a number of structures (including graphs, hypergraphs, hypercubes, graphons, and many more) and works for random variables in $L_p$ for any $p>1$. Our approach is based on martingale difference sequences. Archive classification: math.CO math.FA math.PR Remarks: 24 pages, no figures Submitted from: pdodos at math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5966 or http://arXiv.org/abs/1410.5966

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Gerard Buskes and Chris Schwanke From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 12 Nov 2014 15:20:30 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Functional completions of archimedean vector lattices" by Gerard Buskes and Chris Schwanke. Abstract: We study completions of Archimedean vector lattices relative to any nonempty set of positively-homogeneous functions on finite-dimensional real vector spaces. Examples of such completions include square mean closed and geometric closed vector lattices, amongst others. These functional completions also lead to a universal definition of the complexification of any Archimedean vector lattice and a theory of tensor products and powers of complex vector lattices in a companion paper. Archive classification: math.FA Mathematics Subject Classification: 06F20, 46A40 Submitted from: mmbuskes at olemiss.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.5878 or http://arXiv.org/abs/1410.5878

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Afonso S. Bandeira, Dustin G. Mixon, and Joel Moreira From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 12:40:31 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "A conditional construction of restricted isometries" by Afonso S. Bandeira, Dustin G. Mixon, and Joel Moreira. Abstract: We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $\epsilon>0$ such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter $K=\Omega(M^{1/2+\epsilon})$, where $M$ is the number of rows. Archive classification: math.FA cs.IT math.IT math.NT Remarks: 6 pages Submitted from: moreira at math.ohio-state.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.6457 or http://arXiv.org/abs/1410.6457

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by E. Casini, E. Miglierina, and L. Piasecki From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 12:44:13 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Hyperplanes in the space of convergent sequences and preduals of $\ell_1$" by E. Casini, E. Miglierina, and L. Piasecki. Abstract: The main aim of the present paper is to investigate various structural properties of hyperplanes of $c$, the Banach space of the convergent sequences. In particular, we give an explicit formula for the projection constants and we prove that an hyperplane of $c$ is isometric to the whole space if and only if it is $1$-complemented. Moreover, we obtain the classification of those hyperplanes for which their duals are isometric to $\ell_{1}$ and we give a complete description of the preduals of $\ell_{1}$ under the assumption that the standard basis of $\ell_{1}$ is weak$^{*}$-convergent. Archive classification: math.FA Mathematics Subject Classification: 46B45 (Primary), 46B04 (Secondary) Submitted from: enrico.miglierina at unicatt.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.7801 or http://arXiv.org/abs/1410.7801

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Richard Lechner and Paul F.X. Mueller From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 12:47:52 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Localization and projections on bi--parameter BMO" by Richard Lechner and Paul F.X. Mueller. Abstract: We prove that for any operator T on bi--parameter BMO the identity factors through T or Id - T. As a consequence, bi--parameter BMO is a primary Banach space. Bourgain's localization method provides the conceptual framework of our proof. It consists in replacing the factorization problem on the non--separable Banach space bi--parameter BMO by its localized, finite dimensional counterpart. We solve the resulting finite dimensional factorization problems by combinatorics of colored dyadic rectangles. Archive classification: math.FA Mathematics Subject Classification: 46B25, 60G46, 46B07, 46B26, 30H35 Submitted from: Richard.Lechner at jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.8786 or http://arXiv.org/abs/1410.8786

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Cwikel and Richard Rochberg From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 14:22:39 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Lecture notes on complex interpolation of compactness" by Michael Cwikel and Richard Rochberg. Abstract: Suppose that the linear operator $T$ maps $X_0$ compactly to $Y_0$ and also maps $X_1$ boundedly to $Y_1$. We deal once again with the 51 year old question of whether $T$ also always maps the complex interpolation space $[X_0,X_1]_\theta$ compactly to $[Y_0,Y_1]_\theta$. This is a short preliminary version of our promised technical sequel to our earlier paper arXiv:1410.4527 on this topic. It contains the following two small new partial results: (i) The answer to the above question is yes, in the particular case where $Y_0$ is a UMD-space. (ii) The answer to the above question is yes for given spaces $X_0$, $X_1$, $Y_0$ and $Y_1$ if the answer to the "dualized" or "adjoint" version of the question for the duals of these particular spaces is yes. In fact we deduce (i) from (ii) and from an earlier result obtained jointly by one of us with Nigel Kalton. It is remarked that a proof of a natural converse of (ii) would answer the general form of this question completely. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70, 46B50. Secondary 46E15 Remarks: 7 pages 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/1411.0171 or http://arXiv.org/abs/1411.0171 This is an announcement for the paper "An improvement of a theorem of Heinrich, Mankiewicz, Sims, and Yost" by Trond A. Abrahamsen. Abstract: Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space Y is contained in a separable ideal in Y. We improve this result by replacing the term "ideal" with the term "almost isometric ideal". As a consequence of this we obtain, in terms of subspaces, characterizations of diameter 2 properties, the Daugavet property along with the properties of being an almost square space and an octahedral space. Archive classification: math.FA Mathematics Subject Classification: 46B20 (Primary) 46B07 (Secondary) Remarks: 13 pages Submitted from: trond.a.abrahamsen at uia.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.0425 or http://arXiv.org/abs/1411.0425

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Azagra and Carlos Mudarra From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 14:51:22 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Global approximation of convex functions by differentiable convex functions on Banach spaces" by Daniel Azagra and Carlos Mudarra. Abstract: We show that if $X$ is a Banach space whose dual $X^{*}$ has an equivalent locally uniformly rotund (LUR) norm, then for every open convex $U\subseteq X$, for every $\varepsilon >0$, and for every continuous and convex function $f:U \rightarrow \mathbb{R}$ (not necessarily bounded on bounded sets) there exists a convex function $g:X \rightarrow \mathbb{R}$ of class $C^1(U)$ such that $f-\varepsilon\leq g\leq f$ on $U.$ We also show how the problem of global approximation of continuous (not necessarily bounded on bounded sets) and convex functions by $C^k$ smooth convex functions can be reduced to the problem of global approximation of Lipschitz convex functions by $C^k$ smooth convex functions. Archive classification: math.FA Mathematics Subject Classification: 46B20, 52A99, 26B25, 41A30 Remarks: 8 pages Submitted from: dazagra at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.0471 or http://arXiv.org/abs/1411.0471

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Nigel Kalton and Lutz Weis From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 14:53:25 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "The $H^{\infty}$--functional calculus and square function estimates" by Nigel Kalton and Lutz Weis. Abstract: Using notions from the geometry of Banach spaces we introduce square functions $\gamma(\Omega,X)$ for functions with values in an arbitrary Banach space $X$. We show that they have very convenient function space properties comparable to the Bochner norm of $L_2(\Omega,H)$ for a Hilbert space $H$. In particular all bounded operators $T$ on $H$ can be extended to $\gamma(\Omega,X)$ for all Banach spaces $X$. Our main applications are characterizations of the $H^{\infty}$--calculus that extend known results for $L_p$--spaces from \cite{CowlingDoustMcIntoshYagi}. With these square function estimates we show, e.~g., that a $c_0$--group of operators $T_s$ on a Banach space with finite cotype has an $H^{\infty}$--calculus on a strip if and only if $e^{-a|s|}T_s$ is $R$--bounded for some $a > 0$. Similarly, a sectorial operator $A$ has an $H^{\infty}$--calculus on a sector if and only if $A$ has $R$--bounded imaginary powers. We also consider vector valued Paley--Littlewood $g$--functions on $UMD$--spaces. Archive classification: math.FA Submitted from: Lutz.weis at kit.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.0472 or http://arXiv.org/abs/1411.0472

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Pellegrino and Joedson Santos From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 14:56:00 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Lineability and uniformly dominated sets of summing nonlinear" by Daniel Pellegrino and Joedson Santos. Abstract: In this note we prove an abstract version of a result from 2002 due to Delgado and Pi\~{n}ero on absolutely summing operators. Several applications are presented; some of them in the multilinear framework and some in a completely nonlinear setting. In a final section we investigate the size of the set of non uniformly dominated sets of linear operators under the point of view of lineability. Archive classification: math.FA Submitted from: pellegrino at pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.1100 or http://arXiv.org/abs/1411.1100

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Debmalya Sain, Kallol Paul and Kanhaiya Jha From: Dale Alspach <alspach at math.okstate.edu> Date: Fri, 14 Nov 2014 14:58:12 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Strictly convex space : Strong orthogonality and conjugate diameters" by Debmalya Sain, Kallol Paul and Kanhaiya Jha. Abstract: In a normed linear space X an element x is said to be orthogonal to another element y in the sense of Birkhoff-James, written as $ x \perp_{B}y, $ iff $ \| x \| \leq \| x + \lambda y \| $ for all scalars $ \lambda.$ We prove that a normed linear space X is strictly convex iff for any two elements x, y of the unit sphere $ S_X$, $ x \perp_{B}y $ implies $ \| x + \lambda y \| > 1~ \forall~ \lambda \neq 0. $ We apply this result to find a necessary and sufficient condition for a Hamel basis to be a strongly orthonormal Hamel basis in the sense of Birkhoff-James in a finite dimensional real strictly convex space X. Applying the result we give an estimation for lower bounds of $ \| tx+(1-t)y\|, t \in [0,1] $ and $ \| y + \lambda x \|, ~\forall ~\lambda $ for all elements $ x,y \in S_X $ with $ x \perp_B y. $ We find a necessary and sufficient condition for the existence of conjugate diameters through the points $ e_1,e_2 \in ~S_X $ in a real strictly convex space of dimension 2. The concept of generalized conjuagte diameters is then developed for a real strictly convex smooth space of finite dimension. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 47A30 Submitted from: kalloldada at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.1464 or http://arXiv.org/abs/1411.1464

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daher Mohammad From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:42:50 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "K(X,Y) as subspace complemented of L(X,Y)" by Daher Mohammad. Abstract: Let X,Y be two Banach spaces ; in the first part of this work, we show that K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each bounded sequence in Y has a subsequece which is w* convergente. Afterward we obtain some results of M.Feder and G.Emmanuele: Finally in this part we study the relation between the existence of projection from L(X,Y) on K(X,Y) and the existence of pro- jection from K(X,Y ) on K(X,Y) if Y has the approximation property. In the second part we study the Radon-Nikodym property in L(X,Y): Archive classification: math.FA Mathematics Subject Classification: 46EXX Remarks: 21 pages Submitted from: m.daher at orange.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.2217 or http://arXiv.org/abs/1411.2217

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Kasper Green Larsen and Jelani Nelson From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:47:10 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "The Johnson-Lindenstrauss lemma is optimal for linear dimensionality reduction" by Kasper Green Larsen and Jelani Nelson. Abstract: For any $n>1$ and $0<\varepsilon<1/2$, we show the existence of an $n^{O(1)}$-point subset $X$ of $\mathbb{R}^n$ such that any linear map from $(X,\ell_2)$ to $\ell_2^m$ with distortion at most $1+\varepsilon$ must have $m = \Omega(\min\{n, \varepsilon^{-2}\log n\})$. Our lower bound matches the upper bounds provided by the identity matrix and the Johnson-Lindenstrauss lemma, improving the previous lower bound of Alon by a $\log(1/\varepsilon)$ factor. Archive classification: cs.IT cs.CG cs.DS math.FA math.IT Submitted from: minilek at seas.harvard.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.2404 or http://arXiv.org/abs/1411.2404

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Marek Cuth and Michal Doucha From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:48:53 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Lipschitz-free spaces over ultrametric spaces" by Marek Cuth and Michal Doucha. Abstract: We prove that the Lipschitz-free space over a separable ultrametric space has a monotone Schauder basis and is isomorphic to $\ell_1$. This extends results of A. Dalet using an alternative approach. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B15, 54E35 Submitted from: marek.cuth at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.2434 or http://arXiv.org/abs/1411.2434

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikhail I. Ostrovskii From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:51:21 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Metric characterizations of some classes of Banach spaces" by Mikhail I. Ostrovskii. Abstract: The main purpose of the paper is to present some recent results on metric characterizations of superreflexivity and the Radon-Nikod\'ym property. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary 46B85, Secondary: 05C12, 20F67, 30L05, 46B07, 46B22 Submitted from: ostrovsm at stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3366 or http://arXiv.org/abs/1411.3366

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Tengiz Kopaliani, Nino Samashvili and Shalva Zviadadze From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:52:45 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "On the upper and lower estimates of norms in variable exponent spaces" by Tengiz Kopaliani, Nino Samashvili and Shalva Zviadadze. Abstract: In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$ then for the norm of corresponding variable exponent Lebesgue space we have the following lower estimate $$\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}\leq C\|f\|_{p(\cdot)}$$ where $\{Q\}$ defines disjoint partition of $[0;1]$. Also we have constructed variable exponent Lebesgue space with above property which does not possess following upper estimation $$\|f\|_{p(\cdot)}\leq C\left\|\sum \chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}. $$ Archive classification: math.FA Mathematics Subject Classification: 42B35, 42B20, 46B45, 42B25 Remarks: 13 pages Submitted from: sh.zviadadze at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3461 or http://arXiv.org/abs/1411.3461

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Florent Pierre Baudier From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:54:20 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "On the $(\beta)$-distortion of countably branching hyperbolic trees" by Florent Pierre Baudier. Abstract: In this note we show that the distortion incurred by a bi-Lipschitz embedding of the countably branching hyperbolic tree of height $N$ into a Banach space admitting a norm satisfying Rolewicz property $(\beta)$ with power type $p>1$ is at least of the order of $\log(N)^{1/p}$. An application of our result gives a quantitative version of the non-embeddability of countably branching hyperbolic trees into reflexive Banach spaces admitting an equivalent asymptotically uniformly smooth norm and an equivalent asymptotically uniformly convex norm from Baudier, Kalton and Lancien. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 46B85 Remarks: 5 pages Submitted from: florent at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.3915 or http://arXiv.org/abs/1411.3915

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jorge Tomas Rodriguez From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:56:16 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "On the norm of products of polynomials on ultraproduct of Banach spaces" by Jorge Tomas Rodriguez. Abstract: The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of Banach spaces $(X_i)_{\mathfrak U}$. We show that, under certain hypotheses, there is a strong relation between this problem and the same problem for the spaces $X_i$. Archive classification: math.FA Submitted from: jtrodrig at dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.5894 or http://arXiv.org/abs/1411.5894

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Tomasz Kobos From: Dale Alspach <alspach at math.okstate.edu> Date: Wed, 26 Nov 2014 14:58:07 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Hyperplanes of finite-dimensional normed spaces with the maximal relative projection constant" by Tomasz Kobos. Abstract: The \emph{relative projection constant} $\lambda(Y, X)$ of normed spaces $Y \subset X$ is defined as $\lambda(Y, X) = \inf \{ ||P|| : P \in \mathcal{P}(X, Y) \}$, where $\mathcal{P}(X, Y)$ denotes the set of all continuous projections from $X$ onto $Y$. By the well-known result of Bohnenblust for every $n$-dimensional normed space $X$ and its subspace $Y$ of codimension $1$ the inequality $\lambda(Y, X) \leq 2 - \frac{2}{n}$ holds. The main goal of the paper is to study the equality case in the theorem of Bohnenblust. We establish an equivalent condition for the equality $\lambda(Y, X) = 2 - \frac{2}{n}$ and present several applications. We prove that every three-dimensional space has a subspace with the projection constant less than $\frac{4}{3} - 0.0007$. This gives a non-trivial upper bound in the problem posed by Bosznay and Garay. In the general case, we give an upper bound for the number of $(n-1)$-dimensional subspaces with the maximal relative projection constant in terms of the facets of the unit ball of $X$. As a consequence, every $n$-dimensional normed space $X$ has an $(n-1)$-dimensional subspace $Y$ with $\lambda(Y, X) < 2-\frac{2}{n}$. This contrasts with the seperable case in which it is possible that every hyperplane has a maximal possible projection constant. Archive classification: math.FA Mathematics Subject Classification: Primary 41A35, 41A65, 47A30, 52A21 Remarks: 15 pages Submitted from: tkobos at wp.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.6214 or http://arXiv.org/abs/1411.6214

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Gideon Schechtman From: Dale Alspach <alspach at math.okstate.edu> Date: Thu, 27 Nov 2014 19:48:41 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Three observations regarding Schatten p classes" by Gideon Schechtman. Abstract: The paper contains three results, the common feature of which is that they deal with the Schatten $p$ class. The first is a presentation of a new complemented subspace of $C_p$ in the reflexive range (and $p\not= 2$). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of $C_p$ in $C_p^n$ with small $n$ and shows that $\ell_p^k$ nicely embeds into $C_p^n$ only if $n$ is at least proportional to $k$ (and then of course the dimension of $C_p^n$ is at least of order $k^2$). The third result concerns single element of $C_p^n$ and shows that for $p>2$ any $n\times n$ matrix of $C_p$ norm one and zero diagonal admits, for every $\varepsilon>0$, a $k$-paving of $C_p$ norm at most $\varepsilon$ with $k$ depending on $\varepsilon$ and $p$ only. Archive classification: math.FA Mathematics Subject Classification: 47B10, 46B20, 46B28 Submitted from: gideon at weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1411.4427 or http://arXiv.org/abs/1411.4427 _______________________________________________ Banach mailing list Banach at mathdept.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Relations Between Banach Space Theory and Geometric Measure Theory workshop, 08 - 12 June 2015, University of Warwick, UK From: Olga Maleva <O.Maleva at bham.ac.uk> Date: Thu, 27 Nov 2014 15:48:36 +0000 To: "Banach at mathdept.okstate.edu" <Banach at mathdept.okstate.edu>

1st ANNOUNCEMENT OF THE WORKSHOP Relations Between Banach Space Theory and Geometric Measure Theory 08 - 12 June 2015 University of Warwick United Kingdom Plenary speakers include: Jesus M F Castillo (Universidad de Extremadura) Gilles Godefroy (Universit<E9> Paris VI) William B Johnson (Texas A&M University) Assaf Naor* (Princeton University) Mikhail Ostrovskii (St.-John's University) Gideon Schechtman (Weizmann Institute) Thomas Schlumprecht (Texas A&M University) *To be confirmed The homepage of the workshop is: http://tinyurl.com/BanachGMT To register please follow the links on the homepage of the workshop. For further information on the workshop please contact the organisers: * David Preiss <d dot preiss at warwick dot ac dot uk> * Olga Maleva <o dot maleva at bham dot ac dot uk> We expect to be able to cover some expenses for a number of participants. Please read more information on the homepage about the funding. We ask to register your attendance at the workshop by 15 April 2015. The Workshop is supported by a European Research Council grant. _______________________________________________ Banach mailing list Banach at mathdept.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Address Changes From: Dale Alspach <alspach at math.okstate.edu> Date: Mon, 15 Dec 2014 16:19:48 -0600 To: <banach at mathdept.okstate.edu>

The Banach list is changing its address. Messages should be sent to banach at mathdept.okstate.edu. The list location for subscribing or unsubscribing is now https://www.mathdept.okstate.edu/cgi-bin/mailman/listinfo/banach The URL for lists of past postings and other information is https://math.okstate.edu/people/alspach/banach/index.html My current address alspach at math.okstate.edu should continue to work but banach at math.okstate.edu will stop working sometime in the next few weeks. Best Wishes for the New Year, Dale Alspach _______________________________________________ Banach mailing list Banach at mathdept.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Address Changes From: Dale Alspach <alspach at math.okstate.edu> Date: Mon, 15 Dec 2014 16:19:48 -0600 To: <banach at mathdept.okstate.edu>

The Banach list is changing its address. Messages should be sent to banach at mathdept.okstate.edu. The list location for subscribing or unsubscribing is now https://www.mathdept.okstate.edu/cgi-bin/mailman/listinfo/banach The URL for lists of past postings and other information is https://math.okstate.edu/people/alspach/banach/index.html My current address alspach at math.okstate.edu should continue to work but banach at math.okstate.edu will stop working sometime in the next few weeks. Best Wishes for the New Year, Dale Alspach _______________________________________________ Banach mailing list Banach at mathdept.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: [Banach] Banach J. Math Anal and Ann. Funct. Anal. From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:44:37 -0600 To: <banach at mathdept.okstate.edu>

Duke University Press partners with the Tusi Mathematical Research Group to publish the Annals of Functional Analysis (AFA) and the Banach Journal of Mathematical Analysis (BJMA). In 2015, Duke University Press will begin publishing both journals. AFA, started in 2010, and BJMA, started in 2007, are online-only journals included in the prestigious "Reference List Journals" covered by MathSciNet and indexed by Zentralblatt Math, Scopus and Thomson Reuters (ISI). With the start of their 2015 volumes under the guidance of strong editorial boards, the journals will increase in frequency from two to four issues per year. The journals publish research papers and critical survey articles that focus on, but are not limited to, functional analysis, abstract harmonic analysis and operator theory. AFA and BJMA have rapidly established themselves as providing high-level scholarship that addresses important questions in the study of mathematical analysis. The journals are no longer open access but papers will be freely available in Project Euclid 5 years after publication. As before, they will be available on Project Euclid at http://projecteuclid.org/euclid.bjma [1] and http://projecteuclid.org/euclid.afa [2] Editor-in-chief M. S. Moslehian =========================================================== _______________________________________________ Banach mailing list Banach at mathdept.okstate.edu http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Aleksandar Nikolov From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:50:09 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Randomized rounding for the largest $j$-simplex problem" by Aleksandar Nikolov. Abstract: The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{R}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathsf{NP}$-hard to approximate within a factor of $2^{cj}$ for some constant $c$. Our algorithm also approximates the problem of finding the largest determinant principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix, with approximation ratio $e^{j + o(j)}$. We achieve our approximation by rounding solutions to a generlization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid probelm. Our arguments give a short and simple proof of a restricted invertibility principle for determinants. Archive classification: cs.CG cs.DS math.FA Submitted from: anikolov at cs.rutgers.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.0036 or http://arXiv.org/abs/1412.0036

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Astrid Berg, Lukas Parapatits, Franz E. Schuster, and Manuel Weberndorfer From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:52:32 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Log-concavity properties of Minkowski valuations" by Astrid Berg, Lukas Parapatits, Franz E. Schuster, and Manuel Weberndorfer. Abstract: New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are explored. It is shown that both lead to the same class of Minkowski valuations for which these inequalities hold. An appendix by Semyon Alesker contains the proof of a new classification of generalized translation invariant valuations. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A38, 52B45 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/1411.7891 or http://arXiv.org/abs/1411.7891

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Gilles Pisier and Eric Ricard From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:54:03 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "The non-commutative Khintchine inequalities for $0<p<1$" by Gilles Pisier and Eric Ricard. Abstract: We give a proof of the Khintchine inequalities in non-commutative $L_p$-spaces for all $0< p<1$. These new inequalities are valid for the Rademacher functions or Gaussian random variables, but also for more general sequences, e.g. for the analogues of such random variables in free probability. We also prove a factorization for operators from a Hilbert space to a non commutative $L_p$-space, which is new for $0<p<1$. We end by showing that Mazur maps are H\"older on semifinite von Neumann algebras. Archive classification: math.OA math.FA Mathematics Subject Classification: 2000 MSC 46L51, 46L07, 47L25, 47L20 Submitted from: pisier at math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.0222 or http://arXiv.org/abs/1412.0222

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Jarno Talponen From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:55:29 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Uniform-to-proper duality of geometric properties of Banach spaces and their ultrapowers" by Jarno Talponen. Abstract: In this note various geometric properties of a Banach space $X$ are characterized by means of weaker corresponding geometric properties involving an ultrapower $X^\mathcal{U}$. The characterizations do not depend on the particular choice of the free ultrafilter $\mathcal{U}$. For example, a point $x\in S_X$ is an MLUR point if and only if $j(x)$ (given by the canonical inclusion $j\colon X \to X^\mathcal{U}$) in $\B_{X^\mathcal{U}}$ is an extreme point; a point $x\in S_X$ is LUR if and only if $j(x)$ is not contained in any non-degenerate line segment of $S_{X^\mathcal{U}}$; a Banach space $X$ is URED if and only if there are no $x,y \in S_{X^\mathcal{U}}$, $x\neq y$, with $x-y \in j(X)$. Archive classification: math.FA math.LO Mathematics Subject Classification: 03H05, 46B20, 46M07, 46B10 Submitted from: talponen at iki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.1279 or http://arXiv.org/abs/1412.1279

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Michael Megrelishvili From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 10:58:12 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "A note on dependence of families having bounded variation" by Michael Megrelishvili. Abstract: We show that for arbitrary linearly ordered set $X$ any bounded family of real valued functions on $X$ with bounded total variation does not contain independent subsequences. As a corollary we generalize Helly's sequential compactness theorem. Archive classification: math.GN math.FA Mathematics Subject Classification: 54F15, 54D30, 06A05 Remarks: 7 pages Submitted from: megereli at math.biu.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.1515 or http://arXiv.org/abs/1412.1515

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by S. Gabriyelyan, J. Kcakol, W. Kubis, and W. Marciszewski From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 11:00:44 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Networks for the weak topology of Banach and Frechet spaces" by S. Gabriyelyan, J. Kcakol, W. Kubis, and W. Marciszewski. Abstract: We start the systematic study of Fr\'{e}chet spaces which are $\aleph$-spaces in the weak topology. A topological space $X$ is an $\aleph_0$-space or an $\aleph$-space if $X$ has a countable $k$-network or a $\sigma$-locally finite $k$-network, respectively. We are motivated by the following result of Corson (1966): If the space $C_{c}(X)$ of continuous real-valued functions on a Tychonoff space $X$ endowed with the compact-open topology is a Banach space, then $C_{c}(X)$ endowed with the weak topology is an $\aleph_0$-space if and only if $X$ is countable. We extend Corson's result as follows: If the space $E:=C_{c}(X)$ is a Fr\'echet lcs, then $E$ endowed with its weak topology $\sigma(E,E')$ is an $\aleph$-space if and only if $(E,\sigma(E,E'))$ is an $\aleph_0$-space if and only if $X$ is countable. We obtain a necessary and some sufficient conditions on a Fr\'echet lcs to be an $\aleph$-space in the weak topology. We prove that a reflexive Fr\'echet lcs $E$ in the weak topology $\sigma(E,E')$ is an $\aleph$-space if and only if $(E,\sigma(E,E'))$ is an $\aleph_0$-space if and only if $E$ is separable. We show however that the nonseparable Banach space $\ell_{1}(\mathbb{R})$ with the weak topology is an $\aleph$-space. Archive classification: math.FA Mathematics Subject Classification: Primary 46A03, 54H11, Secondary 22A05, 54C35 Remarks: 18 pages Submitted from: kubis at math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.1748 or http://arXiv.org/abs/1412.1748

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by N. Albuquerque, G. Araujo, and D. Pellegrino From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 11:02:33 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "H\"{o}lder's inequality: some recent and unexpected applications" by N. Albuquerque, G. Araujo, and D. Pellegrino. Abstract: H\"{o}lder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and it is, without any doubt, one of the milestones in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this expository article we show how a variant of H\"{o}lder's inequality (although well-known in PDEs) was essentially overlooked in Functional Analysis and has had a crucial (and in some sense unexpected) influence in very recent and major breakthroughs in Mathematics. Some of these recent advances appeared in 2012-2014 and include the theory of Dirichlet series, the famous Bohr radius problem, certain classical inequalities (such as Bohnenblust--Hille or Hardy--Littlewood), or even Mathematical Physics. Archive classification: math.FA Submitted from: pellegrino at pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.2017 or http://arXiv.org/abs/1412.2017

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Tomasz Kania From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 11:04:08 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "On C*-algebras which cannot be decomposed into tensor products with factors infinite-dimensional" by Tomasz Kania. Abstract: We prove that C*-algebras which satisfy a Banach-space property of being a Grothendieck space cannot be decomposed into a tensor product of two infinite-dimensional Banach spaces. By a result of Pfitzner, this class contains all von Neumann algebras and their norm-quotients. We thus strengthen a recent result of Ghasemi who established a similar conclusion for C*-tensor products in the case of SAW*-algebras. In particular, we solve in the negative a problem of Simon Wassermann concerning tensorial decompositions of the Calkin algebra in the category of Banach spaces. Archive classification: math.OA math.FA Submitted from: tomasz.marcin.kania at gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.3621 or http://arXiv.org/abs/1412.3621

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Eusebio Gardella and Hannes Thiel From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 16 Dec 2014 11:05:35 -0600 To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>

This is an announcement for the paper "Quotients of Banach algebras acting on $L^p$-spaces" by Eusebio Gardella and Hannes Thiel. Abstract: We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study of Banach algebras generated by invertible isometries of $L^p$-spaces. Archive classification: math.OA math.FA Mathematics Subject Classification: Primary: 47L10, 43A15. Secondary: 46J10 Remarks: 7 pages Submitted from: gardella at uoregon.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.3985 or http://arXiv.org/abs/1412.3985

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Peide Liu and Maofa Wang From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:29:18 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "Burkholder-Gundy-Davis inequality in martingale Hardy spaces with variable exponent" by Peide Liu and Maofa Wang. Abstract: In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale theory, including convexity lemma, Burkholder-Gundy-Davis' inequality and Chevalier's inequality. Moreover, we investigate some other equivalent relations between variable exponent martingale Hardy spaces. Archive classification: math.FA Submitted from: pdliu at whu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.8146 or http://arXiv.org/abs/1412.8146

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:33:37 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "Almost sure-sign convergence of Hardy-type Dirichlet series" by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris. Abstract: Hartman proved in 1939 that the width of the largest possible strip in the complex plane, on which a Dirichlet series $\sum_n a_n n^{-s}$ is uniformly a.s.-sign convergent (i.e., $\sum_n \varepsilon_n a_n n^{-s}$ converges uniformly for almost all sequences of signs $\varepsilon_n =\pm 1$) but does not convergent absolutely, equals $1/2$. We study this result from a more modern point of view within the framework of so called Hardy-type Dirichlet series with values in a Banach space. Archive classification: math.FA Mathematics Subject Classification: 30B50, 30H10, 46G20 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/1412.5030 or http://arXiv.org/abs/1412.5030

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Liran Rotem From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:35:04 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "A letter: The log-Brunn-Minkowski inequality for complex bodies" by Liran Rotem. Abstract: In this short note we explain why the log-Brunn-Minkowski conjecture is correct for complex convex bodies. We do this by relating the conjecture to the notion of complex interpolation, and appealing to a general theorem by Cordero-Erausquin. Archive classification: math.MG math.FA Submitted from: liranro1 at post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5321 or http://arXiv.org/abs/1412.5321

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Karl-Mikael Perfekt From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:36:06 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "On M-ideals and o-O type spaces" by Karl-Mikael Perfekt. Abstract: We consider pairs of Banach spaces (M_0, M) such that M_0 is defined in terms of a little-o condition, and M is defined by the corresponding big-O condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, M\"obius invariant spaces of analytic functions, Lipschitz-H\"older spaces, etc. It has previously been shown that the bidual M_0** of M_0 is isometrically isomorphic with M. The main result of this paper is that M_0 is an M-ideal in M. This has several useful consequences: M_0 has Pelczynskis properties (u) and (V), M_0 is proximinal in M, and M_0* is a strongly unique predual of M, while M_0 itself never is a strongly unique predual. Archive classification: math.FA Remarks: 9 pages Submitted from: karlmikp at math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5486 or http://arXiv.org/abs/1412.5486

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:37:14 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "On operator relations between locally convex spaces" by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul. Abstract: A linear operator $T:X \to Y$ between vector spaces is called strictly singular if for any infinite dimensional closed vector subspace $M$ of $X$, the restriction of $T$ on $M$ is not a topological isomorphism. In this note we introduced some sufficient conditions on domain and range spaces such that any bounded linear operator in between is strictly singular, and give some examples of spaces satisfying these conditions. Archive classification: math.FA Remarks: 15 pages, presented in the context of 8th Australian and New The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5761 or http://arXiv.org/abs/1412.5761

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Mikhail I. Ostrovskii and Beata Randrianantoanina From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:38:37 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "Metric spaces admitting low-distortion embeddings into all $n$-dimensional Banach spaces" by Mikhail I. Ostrovskii and Beata Randrianantoanina. Abstract: For a fixed $K\gg 1$ and $n\in\mathbb{N}$, $n\gg 1$, we study metric spaces which admit embeddings with distortion $\le K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $\log n$-dimensional Euclidean spaces, and equilateral spaces. We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that any $n$-point ultrametric can be embedded with uniformly bounded distortion into any Banach space of dimension $\log n$. The main result of the paper is a new example of a family of finite metric spaces which are not metric compositions of classical examples and which do embed with uniformly bounded distortion into any Banach space of dimension $n$. This partially answers a question of G.~Schechtman. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12, 30L05, 46B15, 52A21 Remarks: 35 pages, 4 figures Submitted from: randrib at miamioh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.7670 or http://arXiv.org/abs/1412.7670

Return-path: <alspach at math.okstate.edu> Subject: Abstract of a paper by Brendan Pass and Susanna Spektor From: Dale Alspach <alspach at math.okstate.edu> Date: Tue, 30 Dec 2014 17:39:38 -0600 To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>

This is an announcement for the paper "On Khinchine type inequalities for pairwise independent Rademacher random variables" by Brendan Pass and Susanna Spektor. Abstract: We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ pairwise independent Rademacher random variables. We establish that an analogue of Khintchine's inequality cannot hold in this setting with a constant that is independent of $N$; in fact, we prove that the best constant one can hope for is at least $N^{1/2-1/p}$. Furthermore, we show that this estimate is sharp for exchangeable vectors when $p = 4$. As a fortunate consequence of our work, we obtain similar results for $3$-wise independent vectors. Archive classification: math.FA math.PR Submitted from: sanaspek at yandex.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.7859 or http://arXiv.org/abs/1412.7859