Messages from 2015
These are the messages distributed to the Banach list during 2015.
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal Analysis Seminar, March 14-15, 2015
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Wed, 14 Jan 2015 19:05:23 -0500 (18:05 CST)
To: <banach at mathdept.okstate.edu>
Dear Colleague,
The Analysis group at Kent State University is happy to announce
a meeting of the Informal Analysis Seminar, which will be held at the
Department of Mathematical Sciences at Kent State University, March
14-15, 2015.
The plenary lecture series will be given by:
Alexandre Eremenko (Purdue University)
and
Grigoris Paouris (Texas A&M University)
Each speaker will deliver a four hour lecture series designed to be
accessible for graduate students.
Funding is available to cover the local and travel expenses of a limited
number of participants. Graduate students, postdoctoral researchers,
and members of underrepresented groups are particularly encouraged to
apply for support.
A poster session will be held for researchers to display their work.
Graduate students are particularly encouraged to submit a poster.
Posters can be submitted electronically in PDF format.
Further information, and an online registration form, can be found
online http://www.math.kent.edu/informal
We encourage you to register as soon as possible, but to receive support
and/or help with hotel reservation, please, register before February 15,
2014.
Please feel free to contact us at informal at math.kent.edu for any
further information.
Attached is a poster that you are welcome to forward to any colleagues
you think may be interested.
Sincerely,
Analysis Group at Kent State University
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Subject: Abstract of a paper by Alexander Koldobsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 11:53:46 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Slicing inequalities for measures
of convex bodies" by Alexander Koldobsky.
Abstract:
We consider a generalization of the hyperplane problem to arbitrary
measures in place of volume and to sections of lower dimensions. We prove
this generalization for unconditional convex bodies and for duals of
bodies with bounded volume ratio. We also prove it for arbitrary symmetric
convex bodies under the condition that the dimension of sections is less
than $\lambda n$ for some $\lambda\in (0,1).$ The constant depends only
on $\lambda.$ Finally, we show that the behavior of the minimal sections
for some measures may be different from the case of volume.
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/1412.8550
or
http://arXiv.org/abs/1412.8550
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anthony Weston
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 12:22:35 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An application of virtual
degeneracy to two-valued subsets of $L_{p}$-spaces" by Anthony Weston.
Abstract:
Suppose $0 < p < 2$ and that $(\Omega, \mu)$ is a measure space
for which $L_{p}(\Omega, \mu)$ is at least two-dimensional. Kelleher,
Miller, Osborn and Weston have shown that if a subset $B$ of
$L_{p}(\Omega, \mu)$ does not have strict $p$-negative type, then $B$
is affinely dependent (when $L_{p}(\Omega, \mu)$ is considered as a
real vector space). Examples show that the converse of this statement
is not true in general. In this note we describe a class of subsets of
$L_{p}(\Omega, \mu)$ for which the converse statement holds. We prove that
if a two-valued set $B \subset L_{p}(\Omega, \mu)$ is affinely dependent
(when $L_{p}(\Omega, \mu)$ is considered as a real vector space), then
$B$ does not have strict $p$-negative type. This result is peculiar to
two-valued subsets of $L_{p}(\Omega, \mu)$ and generalizes an elegant
theorem of Murugan. It follows, moreover, that of certain types of
isometry with range in $L_{p}(\Omega, \mu)$ cannot exist.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B85
Remarks: 3 page note
Submitted from: westona at canisius.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.8481
or
http://arXiv.org/abs/1412.8481
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 12:47:40 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the optimal constants of the
Bohnenblust--Hille and inequalities" by Daniel Pellegrino.
Abstract:
We find the optimal constants of the generalized Bohnenblust--Hille
inequality for $m$-linear forms over $\mathbb{R}$ and with multiple
exponents $ \left( 1,2,...,2\right)$, sometimes called mixed $\left(
\ell _{1},\ell _{2}\right) $-Littlewood inequality. We show that these
optimal constants are precisely $\left( \sqrt{2}\right) ^{m-1}$ and this
is somewhat surprising since a series of recent papers have shown that the
constants of the Bohnenblust--Hille inequality have a sublinear growth,
and in several cases the same growth was obtained for the constants of
the generalized Bohnenblust--Hille inequality. This result answers a
question raised by Albuquerque et al. (2013) in a paper published in
2014 in the Journal of Functional Analysis. We also improve the best
known constants of the generalized Hardy--Littlewood inequality in such a
way that an unnatural behavior of the old estimates (that will be clear
along the paper) does not happen anymore.
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/1501.00965
or
http://arXiv.org/abs/1501.00965
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Erhan Caliskan and Pilar Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:08:42 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "s-Numbers sequences for homogeneous
polynomials" by Erhan Caliskan and Pilar Rueda.
Abstract:
We extend the well known theory of $s$-numbers of linear operators to
homogeneous polynomials defined between Banach spaces.
Approximation, Kolmogorov and Gelfand numbers of polynomials are
introduced and some well-known results of the linear and multilinear
settings are obtained for homogeneous polynomials.
Archive classification: math.FA
Submitted from: pilar.rueda at uv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.00785
or
http://arXiv.org/abs/1501.00785
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: Fri, 16 Jan 2015 13:17:33 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the divergence of greedy
algorithms with respect to Walsh subsystems in $L$" by Sergo
A. Episkoposian.
Abstract:
In this paper we prove that there exists a function which $f(x)$ belongs
to $L^1[0,1]$ such that a greedy algorithm
with regard to the Walsh subsystem does not converge to $f(x)$ in
$L^1[0,1]$ norm, i.e. the Walsh subsystem $\{W_{n_k}\}$ is not a
quasi-greedy basis in its linear span in $L^1$
Archive classification: math.FA
Citation: Journal of Nonlinear Analysis Series A: Theory, Methods &
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.00832
or
http://arXiv.org/abs/1501.00832
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vladimir G. Troitsky and Foivos Xanthos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:20:10 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Spaces of regular abstract
martingales" by Vladimir G. Troitsky and Foivos Xanthos.
Abstract:
In \cite{Troitsky:05,Korostenski:08}, the authors introduced and
studied the space $\mathcal M_r$ of regular martingales on a vector
lattice and the space $M_r$ of bounded regular martingales on a Banach
lattice. In this note, we study these two spaces from the vector lattice
point of view. We show, in particular, that these spaces need not be
vector lattices. However, if the underlying space is order complete then
$\mathcal M_r$ is a vector lattice and $M_r$ is a Banach lattice under
the regular norm.
Archive classification: math.FA
Submitted from: foivos at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.01685
or
http://arXiv.org/abs/1501.01685
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bin Han and Zhiqiang Xu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:25:02 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Robustness properties of
dimensionality reduction with gaussian random matrices" by Bin Han and
Zhiqiang Xu.
Abstract:
In this paper we study the robustness properties of dimensionality
reduction with Gaussian random matrices having arbitrarily erased
rows. We first study the robustness property against erasure for
the almost norm preservation property of Gaussian random matrices by
obtaining the optimal estimate of the erasure ratio for a small given
norm distortion rate. As a consequence, we establish the robustness
property of Johnson-Lindenstrauss lemma and the robustness property
of restricted isometry property with corruption for Gaussian random
matrices. Secondly, we obtain a sharp estimate for the optimal lower
and upper bounds of norm distortion rates of Gaussian random matrices
under a given erasure ratio. This allows us to establish the strong
restricted isometry property with the almost optimal RIP constants,
which plays a central role in the study of phaseless compressed sensing.
Archive classification: cs.IT math.FA math.IT math.NA math.PR
Remarks: 22 pages
Submitted from: xuzq at lsec.cc.ac.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.01695
or
http://arXiv.org/abs/1501.01695
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Leandro Candido and Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:27:02 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On complemented copies of
$c_0(\omega_1)$ in $C(K^n)$ spaces" by Leandro Candido and Piotr
Koszmider.
Abstract:
Given a compact Hausdorff space $K$ we consider the Banach space of real
continuous functions $C(K^n)$ or equivalently the $n$-fold injective
tensor product $\hat\bigotimes_{\varepsilon}C(K)$ or the Banach
space of vector valued continuous functions $C(K, C(K, C(K ...,
C(K)...)$. We address the question of the existence of complemented
copies of $c_0(\omega_1)$ in $\hat\bigotimes_{\varepsilon}C(K)$
under the hypothesis that $C(K)$ contains an isomorphic copy of
$c_0(\omega_1)$. This is related to the results of E. Saab and P. Saab
that $X\hat\otimes_\varepsilon Y$ contains a complemented copy of $c_0$,
if one of the infinite dimensional Banach spaces $X$ or $Y$ contains
a copy of $c_0$ and of E. M. Galego and J. Hagler that it follows from
Martin's Maximum that if $C(K)$ has density $\omega_1$ and contains a
copy of $c_0(\omega_1)$, then $C(K\times K)$ contains a complemented
copy $c_0(\omega_1)$.
The main result is that under the assumption of $\clubsuit$ for every
$n\in N$ there is a compact Hausdorff space $K_n$ of weight $\omega_1$
such that $C(K)$ is Lindel\"of in the weak topology, $C(K_n)$ contains a
copy of $c_0(\omega_1)$, $C(K_n^n)$ does not contain a complemented copy
of $c_0(\omega_1)$ while $C(K_n^{n+1})$ does contain a complemented copy
of $c_0(\omega_1)$. This shows that additional set-theoretic assumptions
in Galego and Hagler's nonseparable version of Cembrano and Freniche's
theorem are necessary as well as clarifies in the negative direction the
matter unsettled in a paper of Dow, Junnila and Pelant whether half-pcc
Banach spaces must be weakly pcc.
Archive classification: math.FA math.GN math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.01785
or
http://arXiv.org/abs/1501.01785
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigory Ivanov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:28:47 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Convex hull deviation and
contractibility" by Grigory Ivanov.
Abstract:
We study the Hausdorff distance between a set and its convex hull. Let
$X$ be a Banach space, define the CHD-module of space $X$ as the supremum
of this distance for all subset of the unit ball in $X$. In the case of
finite dimensional Banach spaces we obtain the exact upper bound of the
CHD-module depending on the dimension of the space. We give an upper
bound for the CHD-module in $L_p$ spaces. We prove that CHD-module
is not greater than the maximum of the Lipschitz constants of metric
projection operator onto hyperplanes. This implies that for a Hilbert
space CHD-module equals 1. We prove criterion of the Hilbert space and
study the contractibility of proximally smooth sets in uniformly convex
and uniformly smooth Banach spaces.
Archive classification: math.FA
Submitted from: grigory.ivanov at phystech.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.02596
or
http://arXiv.org/abs/1501.02596
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan Rozendaal, Fedor Sukochev and Anna Tomskova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:31:35 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Operator Lipschitz functions on
Banach spaces" by Jan Rozendaal, Fedor Sukochev and Anna Tomskova.
Abstract:
Let $X$, $Y$ be Banach spaces and let $\mathcal{L}(X,Y)$ be the
space of bounded linear operators from $X$ to $Y$. We develop
the theory of double operator integrals on $\mathcal{L}(X,Y)$
and apply this theory to obtain commutator estimates of the form
\begin{align*} \|f(B)S-Sf(A)\|_{\mathcal{L}(X,Y)}\leq \textrm{const}
\|BS-SA\|_{\mathcal{L}(X,Y)} \end{align*} for a large class of functions
$f$, where $A\in\mathcal{L}(X)$, $B\in \mathcal{L}(Y)$ are scalar type
operators and $S\in \mathcal{L}(X,Y)$. In particular, we establish this
estimate for $f(t):=|t|$ and for diagonalizable operators on $X=\ell_{p}$
and $Y=\ell_{q}$, for $p<q$ and $p=q=1$, and for $X=Y=\mathrm{c}_{0}$. We
also obtain results for $p\geq q$.
We study the estimate above in the setting of Banach ideals in
$\mathcal{L}(X,Y)$. The commutator estimates we derive hold for
diagonalizable matrices with a constant independent of the size of
the matrix.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 47A55, 47A56, secondary 47B47
Remarks: 30 pages
Submitted from: janrozendaalmath at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.03267
or
http://arXiv.org/abs/1501.03267
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider and Cristobal Rodriguez-Porras
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 16 Jan 2015 13:33:19 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On automorphisms of the
Banach space $\ell_\infty/c_0$" by Piotr Koszmider and Cristobal
Rodriguez-Porras.
Abstract:
We investigate Banach space automorphisms
$T:\ell_\infty/c_0\rightarrow\ell_\infty/c_0 $ focusing on
the possibility of representing their fragments of the form
$$T_{B,A}:\ell_\infty(A)/c_0(A)\rightarrow \ell_\infty(B)/c_0(B)$$ for $A,
B\subseteq N$ infinite by means of linear operators from $\ell_\infty(A)$
into $\ell_\infty(B)$, infinite $A\times B$-matrices, continuous maps from
$B^*=\beta B\setminus B$ into $A^*$, or bijections from $B$ to $A$. This
leads to the analysis of general linear operators on $\ell_\infty/c_0$. We
present many examples, introduce and investigate several classes of
operators, for some of them we obtain satisfactory representations and
for other give examples showing that it is impossible. In particular,
we show that there are automorphisms of $\ell_\infty/c_0$ which cannot
be lifted to operators on $\ell_\infty$ and assuming OCA+MA we show that
every automorphism of $\ell_\infty/c_0$ with no fountains or with no
funnels is locally, i.e., for some infinite $A, B\subseteq N$ as above,
induced by a bijection from $B$ to $A$. This additional set-theoretic
assumption is necessary as we show that the continuum hypothesis implies
the existence of counterexamples of diverse flavours. However, many
basic problems, some of which are listed in the last section, remain open.
Archive classification: math.FA
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.03466
or
http://arXiv.org/abs/1501.03466
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Isaac Goldbring and Martino Lupini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:03:22 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Model-theoretic aspects of the
Gurarij operator space" by Isaac Goldbring and Martino Lupini.
Abstract:
We show that the theory of the Gurarij operator space is the
model-completion of the theory of operator spaces, it has a unique
separable $1$-exact model, continuum many separable models, and no
prime model. We also establish the corresponding facts for the Gurarij
operator system. The proofs involve establishing that the theories
of the Fra\"iss\'{e} limits of the classes of finite-dimensional
$M_q$-spaces and $M_q$-systems are separably categorical and have
quantifier-elimination. We conclude the paper by showing that no
existentially closed operator system can be completely order isomorphic
to a C$^*$ algebra.
Archive classification: math.LO math.FA math.OA
Remarks: 21 pages
Submitted from: isaac at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.04332
or
http://arXiv.org/abs/1501.04332
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:05:34 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Preserving affine Baire classes
by perfect affine maps" by Ondrej F.K. Kalenda and Jiri Spurny.
Abstract:
Let $\varphi\colon X\to Y$ be an affine continuous surjection between
compact convex sets. Suppose that the canonical copy of the space of
real-valued affine continuous functions on $Y$ in the space of real-valued
affine continuous functions on $X$ is complemented. We show that if $F$
is a topological vector space, then $f\colon Y\to F$ is of affine Baire
class $\alpha$ whenever the composition $f\circ\varphi$ is of affine
Baire class $\alpha$. This abstract result is applied to extend known
results on affine Baire classes of strongly affine Baire mappings.
Archive classification: math.FA
Mathematics Subject Classification: 46A55, 26A21, 54H05
Remarks: 10 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/1501.05118
or
http://arXiv.org/abs/1501.05118
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: Wed, 28 Jan 2015 13:07:56 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Pythagorean powers of hypercubes"
by Assaf Naor and Gideon Schechtman.
Abstract:
For $n\in \mathbb{N}$ consider the $n$-dimensional hypercube as equal
to the vector space $\mathbb{F}_2^n$, where $\mathbb{F}_2$ is
the field of size two. Endow $\mathbb{F}_2^n$ with the Hamming
metric, i.e., with the metric induced by the $\ell_1^n$ norm
when one identifies $\mathbb{F}_2^n$ with $\{0,1\}^n\subseteq
\mathbb{R}^n$. Denote by $\ell_2^n(\mathbb{F}_2^n)$ the $n$-fold
Pythagorean product of $\mathbb{F}_2^n$, i.e., the space of
all $x=(x_1,\ldots,x_n)\in \prod_{j=1}^n \mathbb{F}_2^n$,
equipped with the metric $$ \forall\, x,y\in \prod_{j=1}^n
\mathbb{F}_2^n,\qquad d_{\ell_2^n(\mathbb{F}_2^n)}(x,y)= \sqrt{
\|x_1-y_1\|_1^2+\ldots+\|x_n-y_n\|_1^2}. $$ It is shown here that the
bi-Lipschitz distortion of any embedding of $\ell_2^n(\mathbb{F}_2^n)$
into $L_1$ is at least a constant multiple of $\sqrt{n}$. This is
achieved through the following new bi-Lipschitz invariant, which
is a metric version of (a slight variant of) a linear inequality
of Kwapie{\'n} and Sch\"utt (1989). Letting $\{e_{jk}\}_{j,k\in
\{1,\ldots,n\}}$ denote the standard basis of the space of all
$n$ by $n$ matrices $M_n(\mathbb{F}_2)$, say that a metric space
$(X,d_X)$ is a KS space if there exists $C=C(X)>0$ such that for
every $n\in 2\mathbb{N}$, every mapping $f:M_n(\mathbb{F}_2)\to
X$ satisfies \begin{equation*}\label{eq:metric KS abstract}
\frac{1}{n}\sum_{j=1}^n\mathbb{E}\left[d_X\Big(f\Big(x+\sum_{k=1}^ne_{jk}\Big),f(x)\Big)\right]\le
C
\mathbb{E}\left[d_X\Big(f\Big(x+\sum_{j=1}^ne_{jk_j}\Big),f(x)\Big)\right],
\end{equation*} where the expectations above are with respect to
$x\in M_n(\mathbb{F}_2)$ and $k=(k_1,\ldots,k_n)\in \{1,\ldots,n\}^n$
chosen uniformly at random. It is shown here that $L_1$ is a KS space
(with $C= 2e^2/(e^2-1)$, which is best possible), implying the above
nonembeddability statement. Links to the Ribe program are discussed,
as well as related open problems.
Archive classification: math.FA math.MG
Submitted from: naor at math.princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.05213
or
http://arXiv.org/abs/1501.05213
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yanni Chen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:09:59 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A General
Beurling-Helson-Lowdenslager Theorem on the Disk" by Yanni Chen.
Abstract:
We give a simple proof of the Beurling-Helson-Lowdenslager invariant
subspace theorem for a very general class of norms on $L^{\infty}\left(
\mathbb{T}% \right) .
Archive classification: math.FA
Submitted from: yanni.chen at unh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.05718
or
http://arXiv.org/abs/1501.05718
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Morten Nielsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:12:24 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On Schauder Bases Properties of
Multiply Generated Gabor Systems" by Morten Nielsen.
Abstract:
Let $A$ be a finite subset of $L^2(\mathbb{R})$ and
$p,q\in\mathbb{N}$. We characterize the Schauder basis properties
in $L^2(\mathbb{R})$ of the Gabor system
$$G(1,p/q,A)=\{e^{2\pi i m x}g(x-np/q) : m,n\in \mathbb{Z}, g\in A\},$$
with a specific ordering on $\mathbb{Z}\times \mathbb{Z}\times A$. The
characterization is given in terms of a Muckenhoupt matrix $A_2$ condition
on an associated Zibulski-Zeevi type matrix.
Archive classification: math.FA
Mathematics Subject Classification: 42C15, 46B15, 42C40
Remarks: 14 pages
Submitted from: mnielsen at math.aau.dk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.05794
or
http://arXiv.org/abs/1501.05794
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hichem Ben-El-Mechaiekh
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:17:31 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Intersection Theorems for Closed
Convex Sets and Applications" by Hichem Ben-El-Mechaiekh.
Abstract:
A number of landmark existence theorems of nonlinear functional analysis
follow in a simple and direct way from the basic separation of
convex closed sets in finite dimension via elementary versions of the
Knaster-Kuratowski-Mazurkiewicz principle - which we extend to arbitrary
topological vector spaces - and a coincidence property for so-called
von Neumann relations. The method avoids the use of deeper results
of topological essence such as the Brouwer fixed point theorem or the
Sperner's lemma and underlines the crucial role played by convexity. It
turns out that the convex KKM principle is equivalent to the Hahn-Banach
theorem, the Markov-Kakutani fixed point theorem, and the Sion-von
Neumann minimax principle.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 52A07, 32F32, 32F27,
Secondary: 47H04, 47H10, 47N10
Submitted from: hmechaie at brocku.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.05813
or
http://arXiv.org/abs/1501.05813
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S.K. Mercourakis and G. Vassiliadis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:20:03 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Equilateral Sets in Banach Spaces
of th form C(K)" by S.K. Mercourakis and G. Vassiliadis.
Abstract:
We show that for "most" compact non metrizable spaces, the unit ball
of the Banach space C(K) contains an uncountable 2-equilateral set. We
also give examples of compact non metrizable spaces K such that the
minimum cardinality of a maximal equilateral set in C(K) is countable.
Archive classification: math.FA math.GN
Mathematics Subject Classification: Primary 46B20, 46E15, Secondary
46B26, 54D30
Remarks: 17 pages, overlap with arxiv: 1111.2273 v1
Submitted from: smercour at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.06381
or
http://arXiv.org/abs/1501.06381
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 28 Jan 2015 13:21:17 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Concerning the Szlenk index"
by Ryan Causey.
Abstract:
We discuss pruning and coloring lemmas on regular families. We discuss
several applications of these lemmas to computing the Szlenk index
of certain $w^*$ compact subsets of the dual of a separable Banach
space. Applications include estimates of the Szlenk index of Minkowski
sums, infinite direct sums of separable Banach spaces, constant reduction,
and three space properties.
We also consider using regular families to construct Banach spaces with
prescribed Szlenk index. As a consequence, we give a characterization
of which countable ordinals occur as the Szlenk index of a Banach space,
prove the optimality of a previous universality result, and compute the
Szlenk index of the injective tensor product of separable Banach spaces.
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/1501.06885
or
http://arXiv.org/abs/1501.06885
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eva Pernecka and Richard J. Smith
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:09:38 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Metric Approximation Property
and Lipschitz-Free Spaces over Subsets of $\mathbb{R}^N$" by Eva Pernecka
and Richard J. Smith.
Abstract:
We prove that for certain subsets $M \subseteq \mathbb{R}^N$,
$N \geqslant 1$, the Lipschitz-free space $\mathcal{F}(M)$ has the
metric approximation property (MAP), with respect to any norm on
$\mathbb{R}^N$. In particular, $\mathcal{F}(M)$ has the MAP whenever $M$
is a finite-dimensional compact convex set. This should be compared with
a recent result of Godefroy and Ozawa, who showed that there exists
a compact convex subset $M$ of a separable Banach space, for which
$\mathcal{F}(M)$ fails the approximation property.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B28
Submitted from: richard.smith at maths.ucd.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.07036
or
http://arXiv.org/abs/1501.07036
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Farhad Jafari and Tyrrell B. McAllister
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:11:35 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Ellipsoidal cones in normed vector
spaces" by Farhad Jafari and Tyrrell B. McAllister.
Abstract:
We give two characterizations of cones over ellipsoids in real normed
vector spaces. Let $C$ be a closed convex cone with nonempty interior
such that $C$ has a bounded section of codimension $1$. We show that
$C$ is a cone over an ellipsoid if and only if every bounded section
of $C$ has a center of symmetry. We also show that $C$ is a cone
over an ellipsoid if and only if the affine span of $\partial C \cap
\partial(a - C)$ has codimension $1$ for every point $a$ in the interior
of $C$. These results generalize the finite-dimensional cases proved in
(Jer\'onimo-Castro and McAllister, 2013).
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary 46B20, Secondary 52A50,
46B40, 46B10
Remarks: 10 pages, 1 figure
Submitted from: tmcallis at uwyo.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1501.07493
or
http://arXiv.org/abs/1501.07493
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by F. Abtahi, H. G. Amini, H. A. Lotfi, and A. Rejali
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:13:39 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Some intersections of Lorentz
spaces" by F. Abtahi, H. G. Amini, H. A. Lotfi, and A. Rejali.
Abstract:
Let (X,\mu) be a measure space. For p, q\in (0,\infty] and arbitrary
subsets P,Q of (0,\infty], we introduce and characterize some
intersections of Lorentz spaces, denoted by ILp,Q(X,\mu), ILJ,q(X,\mu)
and ILJ,Q(X,\mu).
Archive classification: math.FA
Mathematics Subject Classification: 43A15, 43A20
Remarks: 10 pages, 0 figures
Submitted from: f.abtahi at sci.ui.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.00159
or
http://arXiv.org/abs/1502.00159
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by H. Ardakani and S.M.S. Modarres Mosadegh
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:16:47 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Order almost Dunford-Pettis
Operators on Banach lattices" by H. Ardakani and S.M.S. Modarres Mosadegh.
Abstract:
By introducing the concepts of order almost Dunford-Pettis and almost
weakly limited operators in Banach lattices, we give some properties
of them related to some well known classes of operators, such as, order
weakly compact, order Dunford-Pettis, weak and almost Dunford-Pettis and
weakly limited operators. Then, we characterize Banach lattices E and F
on which each operator from E into F that is order almost Dunford-Pettis
and weak almost Dunford-Pettis is an almost weakly limited operator.
Archive classification: math.FA
Submitted from: h_ardakani at stu.yazd.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.00369
or
http://arXiv.org/abs/1502.00369
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergio Solimini and Cyril Tintarev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:18:13 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Concentration analysis in Banach
spaces" by Sergio Solimini and Cyril Tintarev.
Abstract:
The concept of a profile decomposition formalizes concentration
compactness arguments on the functional-analytic level, providing
a powerful refinement of the Banach-Alaoglu weak-star compactness
theorem. We prove existence of profile decompositions for general
bounded sequences in uniformly convex Banach spaces equipped with
a group of bijective isometries, thus generalizing analogous results
previously obtained for Sobolev spaces and for Hilbert spaces. Profile
decompositions in uniformly convex Banach spaces are based on the notion
of $\Delta$-convergence by T. C. Lim instead of weak convergence, and
the two modes coincide if and only if the norm satisfies the well-known
Opial condition, in particular, in Hilbert spaces and $\ell^{p}$-spaces,
but not in $L^{p}(\mathbb R^{N})$, $p\neq2$. $\Delta$-convergence
appears naturally in the context of fixed point theory for non-expansive
maps. The paper also studies connection of $\Delta$-convergence with
Brezis-Lieb Lemma and gives a version of the latter without an assumption
of convergence a.e.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B10, 46B50, 46B99
Submitted from: tintarev at math.uu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.00414
or
http://arXiv.org/abs/1502.00414
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Bonet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:19:44 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Abscissas of weak convergence of
vector valued Dirichlet series" by Jose Bonet.
Abstract:
The abscissas of convergence, uniform convergence and absolute
convergence of vector valued Dirichlet series with respect to the original
topology and with respect to the weak topology $\sigma(X,X')$ of a locally
convex space $X$, in particular of a Banach space $X$, are compared. The
relation of their coincidence with geometric or topological properties
of the underlying space $X$ is investigated. Cotype in the context of
Banach spaces, and nuclearity and certain topological invariants for
Fr\'echet spaces play a relevant role.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46A04, secondary: 30B50,
32A05, 46A03, 46A11, 46B07
Submitted from: jbonet at mat.upv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.00418
or
http://arXiv.org/abs/1502.00418
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geraldo Botelho and Jamilson R. Campos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:21:02 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Type and cotype of multilinear
operators" by Geraldo Botelho and Jamilson R. Campos.
Abstract:
We introduce the notions of type and cotype of multilinear operators
between Banach spaces and the resulting classes of such mappings are
studied in the setting of the theory of Banach/quasi-Banach ideals
of multilinear operators. Distinctions between the linear and the
multilinear theories are pointed out, typical multilinear features of the
theory are emphasized and many illustrative examples are provided. The
classes we introduce are related to the multi-ideals generated by the
linear ideals of operators of some type/cotype and are proved to be
maximal and Aron-Berner stable.
Archive classification: math.FA
Submitted from: jamilson at dce.ufpb.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.00440
or
http://arXiv.org/abs/1502.00440
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:22:32 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Some alternative definitions
for the ''plus-minus'' interpolation spaces $\left\langle
A_{0},A_{1}\right\rangle _{\theta}$ of Jaak Peetre" by Michael Cwikel.
Abstract:
The Peetre "plus-minus" interpolation spaces $\left\langle
A_{0},A_{1}\right\rangle _{\theta}$ are defined variously via conditions
about the unconditional convergence of certain Banach space valued series
whose terms have coefficients which are powers of 2 or, alternatively,
powers of e. It may seem intuitively obvious that using powers of 2,
or of e, or powers of some other constant number greater than 1 in
such definitions should produce the same space to within equivalence
of norms. To allay any doubts, we here offer an explicit proof of this
fact, via a "continuous" definition of the same spaces where integrals
replace the above mentioned series. This apparently new definition,
which is also in some sense a "limiting case" of the above mentioned
"discrete" definitions, may be relevant in the study of the connection
between the Peetre "plus-minus" interpolation spaces and Calderon complex
interpolation spaces when both the spaces of the underlying couple are are
Banach lattices on the same measure space. Related results can probably
be obtained for the Gustavsson-Peetre variant of the "plus-minus" spaces.
Archive classification: math.FA
Mathematics Subject Classification: 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/1502.00986
or
http://arXiv.org/abs/1502.00986
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles and Witold Marciszewski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:24:17 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Extension operators on balls and
on spaces of finite sets" by Antonio Aviles and Witold Marciszewski.
Abstract:
We study extension operators between spaces $\sigma_n(2^X)$ of subsets
of $X$ of cardinality at most $n$. As an application, we show that if
$B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with
the weak topology, then, for any $0<\lambda<\mu$, there is no extension
operator $T: C(\lambda B_H)\to C(\mu B_H)$.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.01875
or
http://arXiv.org/abs/1502.01875
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Pilar Rueda and Enrique
Sanchez-Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 9 Feb 2015 13:26:28 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Improving integrability via
absolute summability: a general version of Diestel's Theorem" by Daniel
Pellegrino, Pilar Rueda and Enrique Sanchez-Perez.
Abstract:
A classical result by J. Diestel establishes that the composition of a
summing operator with a (strongly measurable) Pettis integrable
function gives a Bochner integrable function. In this paper we show
that a much more general result is possible regarding the improvement of
the integrability of vector valued functions by the summability of the
operator. After proving a general result, we center our attention in the
particular case given by the $(p,\sigma)$-absolutely continuous operators,
that allows to prove a lot of special results on integration improvement
for selected cases of classical Banach spaces ---including $C(K)$, $L^p$
and Hilbert spaces--- and operators ---$p$-summing, $(q,p)$-summing and
$p$-approximable 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/1502.01970
or
http://arXiv.org/abs/1502.01970
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hossein Dehghan
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:07:41 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Characterizing of Inner Product
Spaces by the Mapping $n_{x,y}$" by Hossein Dehghan.
Abstract:
For the vectors $x$ and $y$ in a normed linear spaces $X$, the mapping
$n_{x,y}: \mathbb{R}\to \mathbb{R}$ is defined by
$n_{x,y}(t)=\|x+ty\|$. In this note, comparing the mappings $n_{x,y}$
and $n_{y,x}$ we obtain a simple and useful characterization of inner
product spaces.
Archive classification: math.FA math.CA
Submitted from: hossein.dehgan at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.02250
or
http://arXiv.org/abs/1502.02250
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eftychios Glakousakis and Sophocles
Mercourakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:10:12 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Examples of infinite dimensional
Banach spaces without infinite equilateral sets" by Eftychios Glakousakis
and Sophocles Mercourakis.
Abstract:
An example of an infinite dimensional and separable Banach space
is given, that is not isomorphic to a subspace of l1 with no infinite
equilateral sets.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04
Remarks: 22 pages
Submitted from: smercour at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.02500
or
http://arXiv.org/abs/1502.02500
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Aude Dalet, Pedro L. Kaufmann, and Antonin
Prochazka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:17:48 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Free spaces over ultrametric
spaces are never isometric to $\ell_1$" by Aude Dalet, Pedro L. Kaufmann,
and Antonin Prochazka.
Abstract:
We show that the Lipschitz free space over an ultrametric space is not
isometric to $\ell_1(\Gamma)$ for any set $\Gamma$.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20
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/1502.02719
or
http://arXiv.org/abs/1502.02719
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kaminska and Damian Kubiak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:21:40 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Daugavet property in the
Musielak-Orlicz spaces" by Anna Kaminska and Damian Kubiak.
Abstract:
We show that among all Musielak-Orlicz function spaces on a
$\sigma$-finite non-atomic complete measure space equipped with
either the Luxemburg norm or the Orlicz norm the only spaces with the
Daugavet property are $L_1$, $L_{\infty}$, $L_1\oplus_1 L_{\infty}$
and $L_1\oplus_{\infty} L_{\infty}$. We obtain in particular complete
characterizations of the Daugavet property in the weighted interpolation
spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the
Orlicz spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E30, 47B38
Remarks: 20 pages. To appear in Journal of Mathematical Analysis and
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.02760
or
http://arXiv.org/abs/1502.02760
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daria Ghilli and Paolo Salani
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:23:50 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Quantitative Borell-Brascamp-Lieb
inequalities for compactly power concave functions (and some
applications)" by Daria Ghilli and Paolo Salani.
Abstract:
We strengthen, in two different ways, the so called Borell-Brascamp-
Lieb inequality in the class of power concave functions with compact
support. As examples of applications we obtain two quantitative versions
of the Brunn- Minkowski inequality and of the Urysohn inequality for
torsional rigidity.
Archive classification: math.AP math.FA
Submitted from: ghilli at math.unipd.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.02810
or
http://arXiv.org/abs/1502.02810
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson, Tomasz Kania, and
Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:26:34 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Closed ideals of operators on and
complemented subspaces of Banach spaces of functions with countable
support" by William B. Johnson, Tomasz Kania, and Gideon Schechtman.
Abstract:
Let $\lambda$ be an infinite cardinal number and let
$\ell_\infty^c(\lambda)$ denote the subspace of $\ell_\infty(\lambda)$
consisting of all functions which assume at most countably many non zero
values. We classify all infinite dimensional complemented subspaces
of $\ell_\infty^c(\lambda)$, proving that they are isomorphic to
$\ell_\infty^c(\kappa)$ for some cardinal number $\kappa$. Then
we show that the Banach algebra of all bounded linear operators
on $\ell_\infty^c(\lambda)$ or $\ell_\infty(\lambda)$ has the unique
maximal ideal consisting of operators through which the identity operator
does not factor. Using similar techniques, we obtain an alternative
to Daws' approach description of the lattice of all closed ideals of
$\mathscr{B}(X)$, where $X = c_0(\lambda)$ or $X=\ell_p(\lambda)$
for some $p\in [1,\infty)$, and we classify the closed ideals of
$\mathscr{B}(\ell_\infty^c(\lambda))$ that contain the ideal of weakly
compact operators.
Archive classification: 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/1502.03026
or
http://arXiv.org/abs/1502.03026
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yousef Estaremi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:28:14 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "weighted conditional type operators
between different Orlicz spaces" by Yousef Estaremi.
Abstract:
In this note we consider weighted conditional type operators between
different Orlicz spaces and generalized conditional type Holder
inequality that we defined in [2]. Then we give some necessary and
sufficient conditions for boundedness of weighted conditional type
operators. As a consequence we characterize boundedness of weighted
conditional type operators and multiplication operators between different
L^p-spaces. Finally, we give some upper and lower bounds for essential
norm of weighted conditional type operators.
Archive classification: math.FA
Remarks: 13 pages
Submitted from: estaremi at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.03422
or
http://arXiv.org/abs/1502.03422
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dale E. Alspach and Bunyamin Sari
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:30:07 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Separable elastic Banach spaces
are universal" by Dale E. Alspach and Bunyamin Sari.
Abstract:
A Banach space $X$ is elastic if there is a constant $K$ so that
whenever a Banach space $Y$ embeds into $X$, then there is an embedding
of $Y$ into $X$ with constant $K$. We prove that $C[0,1]$ embeds into
separable infinite dimensional elastic Banach spaces, and therefore they
are universal for all separable Banach spaces. This confirms a conjecture
of Johnson and Odell. The proof uses incremental embeddings into $X$
of $C(K)$ spaces for countable compact $K$ of increasing complexity. To
achieve this we develop a generalization of Bourgain's basis index that
applies to unconditional sums of Banach spaces and prove a strengthening
of the weak injectivity property of these $C(K)$ that is realized on
special reproducible bases.
Archive classification: math.FA
Mathematics Subject Classification: 46B03 (primary), 46B25 (secondary)
Remarks: 27 pages
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/1502.03791
or
http://arXiv.org/abs/1502.03791
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Malgorzata M. Czerwinska and Anna Kaminska
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 16 Feb 2015 09:32:22 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "k-Extreme Points in Symmetric
Spaces of Measurable Operators" by Malgorzata M. Czerwinska and Anna
Kaminska.
Abstract:
Let $\mathcal{M}$ be a semifinite von Neumann algebra with a faithful,
normal, semifinite trace $\tau$ and $E$ be a strongly symmetric
Banach function space on $[0,\tau(1))$. We show that an operator
$x$ in the unit sphere of $E\left(\mathcal{M},\tau\right)$ is
$k$-extreme, $k\in\mathbb N$, whenever its singular value function
$\mu(x)$ is $k$-extreme and one of the following conditions hold (i)
$\mu(\infty,x)=\lim_{t\to\infty}\mu(t,x)=0$ or (ii) $n(x)\mathcal{M}
n(x^*)=0$ and $|x|\geq \mu(\infty,x)s(x)$, where $n(x)$ and $s(x)$
are null and support projections of $x$, respectively. The converse is
true whenever $\mathcal{M}$ is non-atomic. The global $k$-rotundity
property follows, that is if $\mathcal{M}$ is non-atomic then $E$
is $k$-rotund if and only if $E\left(\mathcal{M},\tau\right)$ is
$k$-rotund. As a consequence of the noncommutive results we obtain that
$f$ is a $k$-extreme point of the unit ball of the strongly symmetric
function space $E$ if and only if its decreasing rearrangement $\mu(f)$
is $k$-extreme and $|f|\geq \mu(\infty,f)$. We conclude with the corollary
on orbits $\Omega(g)$ and $\Omega'(g)$. We get that $f$ is a $k$-extreme
point of the orbit $\Omega(g)$, $g\in L_1+L_{\infty}$, or $\Omega'(g)$,
$g\in L_1[0,\alpha)$, $\alpha<\infty$, if and only if $\mu(f)=\mu(g)$
and $|f|\geq \mu(\infty,f)$. From this we obtain a characterization of
$k$-extreme points in Marcinkiewicz spaces.
Archive classification: math.FA
Remarks: The final publication is available at Springer via
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.04104
or
http://arXiv.org/abs/1502.04104
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] CBMS conference: "Introduction to the Theory of Valuations
and Convex Sets"
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Tue, 17 Feb 2015 20:44:51 -0500 (19:44 CST)
To: <banach at mathdept.okstate.edu>
Dear Friends,
From August 10-15 2015, the Department of Mathematical Science of Kent
State University will be hosting a CBMS conference, 'An Introduction to
the Theory of Valuations and Convex Sets', with Semyon Alesker from Tel
Aviv University as the main speaker. We hope that you will be able to
participate. There will be additional one hour lectures by:
Joe Fu (University of Georgia)
Franz Schuster (Vienna University of Technology)
Monika Ludwig (Vienna University of Technology)
Gil Solanes (Universitat Autonoma de Barcelona)
Rolf Schneider (Albert-Ludwigs-Universität Freiburg)
Wolfgang Weil (Karlsruher Institute of Technology)
NSF funding is available to cover the local and travel expenses of a
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 at
www.kent.edu/math/cbms2015
We encourage you to register as soon as possible.
Please feel free to contact us at cbms2015 at math.kent.edu for any further
information.
Sincerely,
The Analysis Group at Kent State University
_______________________________________________
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 Donghai Ji, Byunghoon Lee and Qingying Bu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:05:01 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Diagonals of injective tensor
products of Banach lattices with bases" by Donghai Ji, Byunghoon Lee
and Qingying Bu.
Abstract:
In this paper, we show that four main diagonal spaces of injective
tensor products are pairwise isometrically isomorphic. When E is a Banach
lattice, we show that the tensor diagonal of E is a 1-unconditional basic
sequence in both the n-fold injective tensor product of E and the n-fold
symmetric injective tensor product of E.
Archive classification: math.FA
Mathematics Subject Classification: 46M05, 46B28, 46G25
Remarks: 14 pages, 3 figures
Submitted from: yicimaster at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.05012
or
http://arXiv.org/abs/1502.05012
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:06:47 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Proximity to $\ell_p$ and $c_0$
in Banach spaces" by Ryan Causey.
Abstract:
We construct a class of minimal trees and use these trees to establish a
number of coloring theorems on general trees. Among the applications of
these trees and coloring theorems are quantification of the Bourgain
$\ell_p$ and $c_0$ indices, dualization of the Bourgain $c_0$ index,
establishing sharp positive and negative results for constant reduction,
and estimating the Bourgain $\ell_p$ index of an arbitrary Banach space
$X$ in terms of a subspace $Y$ and the quotient $X/Y$.
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/1502.05753
or
http://arXiv.org/abs/1502.05753
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Patrick Cheridito, Michael Kupper and
Ludovic Tangpi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:10:44 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Representation of increasing
convex functionals with countably additive measures" by Patrick Cheridito,
Michael Kupper and Ludovic Tangpi.
Abstract:
We derive two types of representation results for increasing convex
functionals in terms of countably additive measures. The first is
a max-representation of functionals defined on spaces of real-valued
continuous functions and the second a sup-representation of functionals
defined on spaces of real-valued measurable functions.
Archive classification: math.FA
Mathematics Subject Classification: 47H07, 28C05, 28C15
Submitted from: dito at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.05763
or
http://arXiv.org/abs/1502.05763
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:12:26 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Ball generated property of direct
sums of Banach spaces" by Jan-David Hardtke.
Abstract:
A Banach space $X$ is said to have the ball generated property (BGP)
if every closed, bounded, convex subset of $X$ can be written as an
intersection of finite unions of closed balls. In 2002 S. Basu proved
that the BGP is stable under (infinite) $c_0$- and $\ell^p$-sums for
$1<p<\infty$. We will show here that for any absolute, normalised norm
$\|\cdot\|_E$ on $\mathbb{R}^2$ satisfying a certain smoothness condition
the direct sum $X\oplus_E Y$ of two Banach spaces $X$ and $Y$ with
respect to $\|\cdot\|_E$ enjoys the BGP whenever $X$ and $Y$ have the BGP.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 9 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/1502.06224
or
http://arXiv.org/abs/1502.06224
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:13:43 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On different definitions of
numerical range" by Miguel Martin.
Abstract:
We study the relation between the intrinsic and the spatial numerical
ranges with the recently introduced ``approximated'' spatial numerical
range. As main result, we show that the intrinsic numerical range always
coincides with the convex hull of the approximated spatial numerical
range. Besides, we show sufficient conditions and necessary conditions
to assure that the approximated spatial numerical range coincides with
the closure of the spatial numerical range.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A12, Secondary 46B20
Remarks: 9 pages
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.07079
or
http://arXiv.org/abs/1502.07079
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:14:59 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The version for compact operators
of Lindenstrauss properties A and B" by Miguel Martin.
Abstract:
It has been very recently discovered that there are compact linear
operators between Banach spaces which cannot be approximated by norm
attaining operators. The aim of this expository paper is to give an
overview of those examples and also of sufficient conditions ensuring
that compact linear operators can be approximated by norm attaining
operators. To do so, we introduce the analogues for compact operators
of Lindenstrauss properties A and B.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, Secondary 46B20,
46B45, 46B28, 47B07
Remarks: The final publication is available at Springer via
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.07084
or
http://arXiv.org/abs/1502.07084
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson and Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 27 Feb 2015 14:16:38 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A Schauder basis for
$L_1(0,\infty)$ consisting of non-negative functions" by William
B. Johnson and Gideon Schechtman.
Abstract:
We construct a Schauder basis for $L_1$ consisting of non-negative
functions and investigate unconditionally basic and quasibasic sequences
of non-negative functions in $L_p$, $1\le p < \infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B15, 46E30
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/1502.07557
or
http://arXiv.org/abs/1502.07557
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Workshop at A&M
From: Bill Johnson <johnson at math.tamu.edu>
Date: Thu, 5 Mar 2015 15:08:24 -0600
To: <banach at mathdept.okstate.edu>
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2015
The Summer 2015 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 1 to August 2. 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 31 - August 2. Its homepage is located at
http://www.math.tamu.edu/~kerr/workshop/sumirfas2015
July 27 - 31 there will be a Concentration Week, "From Commutators to
BCP Operators", organized by Hari Bercovici and Vern Paulsen.
The meeting will focus on the areas of mathematics developed by Carl
Pearcy,
who is turning 80 this year, and aims to promote connections between
several
different themes in operator theory which have been driving recent
progress in
the subject. Topics will include quasidiagonality, commutators of
operators, and
invariant subspaces. The homepage of the Concentration Week is located at
http://www.math.tamu.edu/~kerr/concweek15
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 "From Commutators to
BCP Operators", please contact Hari Bercovici <bercovic at indiana.edu>
or Vern Paulsen <vern at math.uh.edu>.
_______________________________________________
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: 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, 19 Mar 2015 22:20:54 -0000
To: <Banach at mathdept.okstate.edu>
2nd ANNOUNCEMENT OF THE WORKSHOP
Relations Between Banach Space Theory and Geometric Measure Theory
08 - 12 June 2015
University of Warwick
United Kingdom
Confirmed plenary speakers include:
Jesus M F Castillo (Universidad de Extremadura)
Gilles Godefroy (Université 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)
The homepage of the workshop is: http://tinyurl.com/BanachGMT
To register please follow the links on the homepage of the workshop.
NEW: List of currently registered participants is available on the
website 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.
Please 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: Abstract of a paper by Esteban Andruchow, Eduardo Chiumiento and
Maria Eugenia Di Iorio y Lucero
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 10:10:40 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Proper subspaces and compatibility"
by Esteban Andruchow, Eduardo Chiumiento and Maria Eugenia Di Iorio
y Lucero.
Abstract:
Let $\mathcal{E}$ be a Banach space contained in a Hilbert space
$\mathcal{L}$. Assume that the inclusion is continuous with dense range.
Following the terminology of Gohberg and Zambicki\v{\i}, we say that
a bounded operator on $\mathcal{E}$ is a proper operator if it admits
an adjoint with respect to the inner product of $\mathcal{L}$. By a
proper subspace $\mathcal{S}$ we mean a closed subspace of $\mathcal{E}$
which is the range of a proper projection. If there exists a proper
projection which is also self-adjoint with respect to the inner product
of $\mathcal{L}$, then $\mathcal{S}$ belongs to a well-known class of
subspaces called compatible subspaces. We find equivalent conditions
to describe proper subspaces. Then we prove a necessary and sufficient
condition to ensure that a proper subspace is compatible. Each proper
subspace $\mathcal{S}$ has a supplement $\mathcal{T}$ which is also
a proper subspace. We give a characterization of the compatibility
of both subspaces $\mathcal{S}$ and $\mathcal{T}$. Several examples
are provided that illustrate different situations between proper and
compatible subspaces.
Archive classification: math.FA
Remarks: 18 pages
Submitted from: eduardo at mate.unlp.edu.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.00596
or
http://arXiv.org/abs/1503.00596
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Danie Carando, Andreas Defant, and Pablo
Sevilla-Peris
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 10:12:28 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Some polynomial versions of
cotype and applications" by Danie Carando, Andreas Defant, and Pablo
Sevilla-Peris.
Abstract:
We introduce non-linear versions of the classical cotype of Banach
spaces. We show that spaces with l.u.st and cotype, and that spaces having
Fourier cotype enjoy our non-linear cotype. We apply these concepts to
get results on convergence of vector-valued power series in infinite
many variables and on $\ell_{1}$-multipliers of vector-valued Dirichlet
series. Finally we introduce cotype with respect to indexing sets,
an idea that includes our previous definitions.
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/1503.00850
or
http://arXiv.org/abs/1503.00850
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Veronica Dimant, Santiago
Muro, and Damian Pinasco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 10:14:26 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An integral formula for multiple
summing norms of operators" by Daniel Carando, Veronica Dimant, Santiago
Muro, and Damian Pinasco.
Abstract:
We prove that the multiple summing norm of multilinear operators
defined on some $n$-dimensional real or complex vector spaces with
the $p$-norm may be written as an integral with respect to stables
measures. As an application we show inclusion and coincidence results for
multiple summing mappings. We also present some contraction properties
and compute or estimate the limit orders of this class of operators.
Archive classification: math.FA
Mathematics Subject Classification: 15A69, 15A60, 47B10, 47H60, 46G25
Remarks: 19 pages
Submitted from: smuro at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.01638
or
http://arXiv.org/abs/1503.01638
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eva Pernecka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 11:34:08 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On uniformly differentiable
mappings" by Eva Pernecka.
Abstract:
We are concerned with the rigidity of $\ell_\infty$ and $\ell_\infty^n$
with respect to uniformly differentiable mappings. Our main result
is a non-linear analogy of the classical result on the rigidity of
$\ell_\infty$ with respect to non-weakly compact linear operators by
Rosenthal, and it generalises the theorem on the non-complementability
of $c_0$ in $\ell_\infty$ due to Phillips.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46T20
Submitted from: pernecka at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.03536
or
http://arXiv.org/abs/1503.03536
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kallol Paul, Debmalya Sain and Puja Ghosh
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 11:35:33 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Smoothness of bounded linear
operators" by Kallol Paul, Debmalya Sain and Puja Ghosh.
Abstract:
We prove that for a bounded linear operator $T$ on a Hilbert space
$\mathbb{H},$ $T \bot_B A \Leftrightarrow \langle Tx, Ax \rangle = 0 $
for some $x \in S_{\mathbb{H}}, \|Tx\| = \|T\| $ iff the norm attaining
set $M_T = \{ x \in S_{\mathbb{H}} : \|Tx\| = \|T\|\} $ is a unit sphere
of some finite dimensional subspace $H_0$ of $\mathbb{H}$ i.e., $M_T =
S_{H_0} $ and $\|T\|_{{H_0}^{\bot}} < \|T\|.$ We also prove that if $T$
is a bounded linear operator on a Banach space $\mathbb{X}$ with the norm
attaining set $M_T = D \cup(-D)$ ( $D$ is a non-empty compact connected
subset of $S_{\mathbb{X}}$) and $\sup_{y \in C} \|Ty\| < \|T\|$ for
all closed subsets $C$ of $S_{\mathbb{X}}$ with $d(M_T,C) > 0,$ then $T
\bot_B A \Leftrightarrow Tx \bot_B Ax $ for some $x \in M_T.$ Using these
results we characterize smoothness of compact operators on normed linear
spaces and smoothness of bounded linear operators on Hilbert as well
as Banach spaces. This is for the first time that a characterization
of smoothness of bounded linear operators on a normed linear space
has been obtained. We prove that $T \in B(\mathbb{X}, \mathbb{Y})$
(where $\mathbb{X}$ is a real Banach space and $\mathbb{Y}$ is a real
normed linear space) is smooth iff $T$ attains its norm at unique
(upto muliplication by scalar) vector $ x \in S_{\mathbb{X}},$ $Tx$
is a smooth point of $\mathbb{Y} $ and $\sup_{y \in C} \|Ty\| < \|T\|$
for all closed subsets $C$ of $S_{\mathbb{X}}$ with $d(\pm x,C) > 0.$
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B50
Remarks: 13 pages
Submitted from: kalloldada at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.03683
or
http://arXiv.org/abs/1503.03683
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A.Vershik
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 11:37:04 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Equipped graded graphs, projective
limits of simplices, and their boundaries" by A.Vershik.
Abstract:
In this paper, we develop a theory of equipped graded graphs (or
Bratteli diagrams) and an alternative theory of projective limits of
finite-dimensional simplices. An equipment is an additional structure on
the graph, namely, a system of ``cotransition'' probabilities on the set
of its paths. The main problem is to describe all probability measures
on the path space of a graph with given cotransition probabilities;
it goes back to the problem, posed by E.~B.~Dynkin in the 1960s, of
describing exit and entrance boundaries for Markov chains. The most
important example is the problem of describing all central measures, to
which one can reduce the problems of describing states on AF-algebras
or characters on locally finite groups. We suggest an unification of
the whole theory, an interpretation of the notions of Martin, Choquet,
and Dynkin boundaries in terms of equipped graded graphs and in terms
of the theory of projective limits of simplices. In the last section,
we study the new notion of ``standardness'' of projective limits of
simplices and of equipped Bratteli diagrams, as well as the notion of
``lacunarization.''
Archive classification: math.FA
Mathematics Subject Classification: 37L40, 60J20
Remarks: 21 pp.Ref. 12
Submitted from: avershik at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.04447
or
http://arXiv.org/abs/1503.04447
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Henry Towsner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 11:38:33 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An Inverse Ackermannian Lower
Bound on the Local Unconditionality Constant of the James Space" by
Henry Towsner.
Abstract:
The proof that the James space is not locally unconditional appears
to be non-constructive, since it makes use of an ultraproduct
construction. Using proof mining, we extract a constructive proof
and obtain a lower bound on the growth of the local unconditionality
constants.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 46B15
Submitted from: htowsner at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.04745
or
http://arXiv.org/abs/1503.04745
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Martin Rmoutil
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 Mar 2015 11:39:54 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Norm-attaining functionals and
proximinal subspaces" by Martin Rmoutil.
Abstract:
G. Godefroy asked whether, on any Banach space, the set of
norm-attaining functionals contains a 2-dimensional linear subspace. We
prove that a recent construction due to C.J. Read provides an example of
a space which does not have this property. This is done through a study
of the relation between the following two sentences where X is a Banach
space and Y is a closed subspace of finite codimension in X: (A) Y is
proximinal in X. (B) The annihilator of Y consists of norm-attaining
functionals. We prove that these are equivalent if X is the Read's
space. Moreover, we prove that any non-reflexive Banach space X with
any given closed subspace Y of finite codimension at least 2 admits an
equivalent norm such that (B) is true and (A) is false.
Archive classification: math.FA
Mathematics Subject Classification: 46B10, 46B20, 46B03
Submitted from: martin at rmoutil.eu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.06112
or
http://arXiv.org/abs/1503.06112
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 09:58:54 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Uncountable equilateral sets in
Banach spaces of the form $C(K)$" by Piotr Koszmider.
Abstract:
The paper is concerned with the problem whether a nonseparable
Banach space must contain an uncountable set of vectors such that the
distances between every two distinct vectors of the set are the same. Such
sets are called equilateral. We show that Martin's axiom and the negation
of the continuum hypothesis imply that every nonseparable Banach space
of the form $C(K)$ has an uncountable equilateral set. We also show
that one cannot obtain such a result without an additional set-theoretic
assumption since we construct an example of nonseparable Banach space of
the form $C(K)$ which has no uncountable equilateral set (or equivalently
no uncountable $(1+\varepsilon)$-separated set in the unit sphere for
any $\varepsilon>0$) making another consistent combinatorial assumption.
The compact $K$ is a version of the split interval obtained from
a sequence of functions which behave in an anti-Ramsey manner. It remains
open if there is an absolute example of a nonseparable Banach space
of the form different than $C(K)$ which has no uncountable equilateral
set. It follows from the results of S. Mercourakis, G. Vassiliadis that
our example has an equivalent renorming in which it has an uncountable
equilateral set. It remains open if there are consistent examples which
have no uncountable equilateral sets in any equivalent renorming. It
follows from the results of S. Todorcevic that it is consistent that
every nonseparable Banach space has an equivalent renorming in in which
it has an uncountable equilateral set.
Archive classification: math.FA math.GN math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.06356
or
http://arXiv.org/abs/1503.06356
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sanne ter Horst, Miek Messerschmidt, and
Andre C.M. Ran
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:01:45 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Equivalence after extension
for compact operators on Banach spaces" by Sanne ter Horst, Miek
Messerschmidt, and Andre C.M. Ran.
Abstract:
In recent years the coincidence of the operator relations equivalence
after extension and Schur coupling was settled for the Hilbert space
case, by showing that equivalence after extension implies equivalence
after one-sided extension. In this paper we investigate consequences of
equivalence after extension for compact Banach space operators. We show
that generating the same operator ideal is necessary but not sufficient
for two compact operators to be equivalent after extension. In analogy
with the necessary and sufficient conditions on the singular values for
compact Hilbert space operators that are equivalent after extension, we
prove the necessity of similar relationships between the $s$-numbers of
two compact Banach space operators that are equivalent after extension,
for arbitrary $s$-functions.
We investigate equivalence after extension for operators on
$\ell^{p}$-spaces. We show that two operators that act on different
$\ell^{p}$-spaces cannot be equivalent after one-sided extension. Such
operators can still be equivalent after extension, for instance all
invertible operators are equivalent after extension, however, if one
of the two operators is compact, then they cannot be equivalent after
extension. This contrasts the Hilbert space case where equivalence
after one-sided extension and equivalence after extension are, in fact,
identical relations.
Finally, for general Banach spaces $X$ and $Y$, we investigate
consequences of an operator on $X$ being equivalent after extension to
a compact operator on $Y$. We show that, in this case, a closed finite
codimensional subspace of $Y$ must embed into $X$, and that certain
general Banach space properties must transfer from $X$ to $Y$. We also
show that no operator on $X$ can be equivalent after extension to an
operator on $Y$, if $X$ and $Y$ are essentially incomparable Banach
spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 47A05, 47B10 Secondary:
47L20, 46B03
Submitted from: mmesserschmidt at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.07350
or
http://arXiv.org/abs/1503.07350
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by George Androulakis and Matthew Ziemke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:03:37 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The closedness of the generator
of a semigroup" by George Androulakis and Matthew Ziemke.
Abstract:
We study semigroups of bounded operators on a Banach space such
that the members of the semigroup are continuous with respect to various
weak topologies and we give sufficient conditions for the generator of
the semigroup to be closed with respect to the topologies involved. The
proofs of these results use the Laplace transforms of the semigroup. Thus
we first give sufficient conditions for Pettis integrability of vector
valued functions with respect to scalar measures.
Archive classification: math.FA math-ph math.MP
Submitted from: giorgis at math.sc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.07472
or
http://arXiv.org/abs/1503.07472
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:04:58 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Uncountable sets of unit vectors
that are separated by more than 1" by Tomasz Kania and Tomasz Kochanek.
Abstract:
Let $X$ be a Banach space. We study the circumstances under which there
exists an uncountable set $\mathcal A\subset X$ of unit vectors such
that $\|x-y\|>1$ for distinct $x,y\in \mathcal A$. We prove that
such a set exists if $X$ is quasi-reflexive and non-separable; if $X$
is additionally super-reflexive then one can have $\|x-y\|\geqslant
1+\varepsilon$ for some $\varepsilon>0$ that depends only on $X$. If
$K$ is a compact, Hausdorff space, then $X=C(K)$ contains such a set of
cardinality equal to the density of $X$; this solves a problem left open
by S. K. Mercourakis and G. Vassiliadis.
Archive classification: math.FA math.MG
Remarks: 17 pp
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/1503.08166
or
http://arXiv.org/abs/1503.08166
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuele Casini, Enrico Miglierina, and
Lukasz Piasecki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:07:16 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Separable Lindenstrauss spaces
whose duals lack the weak$^*$ fixed point property for nonexpansive
mappings" by Emanuele Casini, Enrico Miglierina, and Lukasz Piasecki.
Abstract:
In this paper we study the $w^*$-fixed point property for nonexpansive
mappings. First we show that the dual space $X^*$ lacks the
$w^*$-fixed point property whenever $X$ contains an isometric copy of
the space $c$. Then, the main result of our paper provides several
characterizations of weak-star topologies that fail the fixed point
property for nonexpansive mappings in $\ell_1$ space. This result allows
us to obtain a characterization of all separable Lindenstrauss spaces $X$
inducing the failure of $w^*$-fixed point property in $X^*$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47H09, Secondary 46B25
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/1503.08875
or
http://arXiv.org/abs/1503.08875
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigory Ivanov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:08:18 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Modulus of supporting convexity
and supporting smoothness" by Grigory Ivanov.
Abstract:
We introduce the moduli of the supporting convexity and the supporting
smoothness of the Banach space which characterize the deviation of the
unit sphere from an arbitrary supporting hyperplane. We show that the
modulus of supporting smoothness, the Banas modulus, and the modulus of
smoothness are equivalent at zero, respectively the modulus of supporting
convexity is equivalent at zero to the modulus of convexity. We prove
a Day-Nordlander type result for these moduli.
Archive classification: math.FA
Submitted from: grigory.ivanov at phystech.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1503.08912
or
http://arXiv.org/abs/1503.08912
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuele Casini, Enrico Miglierina, and
Lukasz Piasecki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 6 Apr 2015 10:10:20 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A remark on spaces of affine
continuous functions on a simplex" by Emanuele Casini, Enrico Miglierina,
and Lukasz Piasecki.
Abstract:
We present an example of an infinite dimensional separable space
of affine continuous functions on a Choquet simplex that does not contain
a subspace linearly isometric to $c$. This example disproves a result
stated in M. Zippin. On some subspaces of Banach spaces whose duals
are $L_1$ spaces. Proc. Amer. Math. Soc. 23, (1969), 378-385.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, Secondary 46B45, 46B25
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/1503.09088
or
http://arXiv.org/abs/1503.09088
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Raphael Clouatre and Kenneth R. Davidson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 14:50:38 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The unit ball of the predual
of $H^\infty(\mathbb{B}_d)$ has no extreme points" by Raphael Clouatre and
Kenneth R. Davidson.
Abstract:
We identify the exposed points of the unit ball of the dual space of the
ball algebra. As a corollary, we show that the predual of
$H^\infty(\mathbb{B}_d)$ has no extreme points in its unit ball.
Archive classification: math.FA
Remarks: 6 pages
Submitted from: ottokar_1er at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.01016
or
http://arXiv.org/abs/1504.01016
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 14:52:49 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A dual method of constructing
hereditarily indecomposable Banach spaces" by Spiros A. Argyros and
Pavlos Motakis.
Abstract:
A new method of defining hereditarily indecomposable Banach spaces is
presented. This method provides a unified approach for constructing
reflexive HI spaces and also HI spaces with no reflexive subspace. All
the spaces presented here satisfy the property that the composition of
any two strictly singular operators is a compact one. This yields the
first known example of a Banach space with no reflexive subspace such
that every operator has a non-trivial closed invariant subspace.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45, 47A15
Remarks: 41 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/1504.01564
or
http://arXiv.org/abs/1504.01564
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonis Manoussakis and Anna
Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 14:54:24 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Operators in tight by support
Banach spaces" by Antonis Manoussakis and Anna Pelczar-Barwacz.
Abstract:
We answer the question of W.T. Gowers, giving an example of a bounded
operator on a subspace of Gowers unconditional space which is not
a strictly singular perturbation of a restriction of a diagonal
operator. We make some observations on operators in arbitrary tight by
support Banach space, showing in particular that in such space no two
isomorphic infinitely dimensional subspaces form a direct sum.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B15
Remarks: 13 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.02701
or
http://arXiv.org/abs/1504.02701
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Florent P. Baudier and Sheng Zhang
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 14:56:08 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "$(\beta)$-distortion of some
infinite graphs" by Florent P. Baudier and Sheng Zhang.
Abstract:
A distortion lower bound of $\Omega(\log(h)^{1/p})$ is proven for
embedding the complete countably branching hyperbolic tree of height $h$
into a Banach space admitting an equivalent norm satisfying property
$(\beta)$ of Rolewicz with modulus of power type $p\in(1,\infty)$
(in short property ($\beta_p$)). Also it is shown that a distortion
lower bound of $\Omega(\ell^{1/p})$ is incurred when embedding the
parasol graph with $\ell$ levels into a Banach space with an equivalent
norm with property ($\beta_p$). The tightness of the lower bound for
trees is shown adjusting a construction of Matou\v{s}ek to the case of
infinite trees. It is also explained how our work unifies and extends
a series of results about the stability under nonlinear quotients of
the asymptotic structure of infinite-dimensional Banach spaces. Finally
two other applications regarding metric characterizations of asymptotic
properties of Banach spaces, and the finite determinacy of bi-Lipschitz
embeddability problems are discussed.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B85, 46B80, 46B20
Remarks: This article supersedes arXiv:1411.3915 from the first author, 21
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.04250
or
http://arXiv.org/abs/1504.04250
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Gabriyelyan, J. Kakol, and G. Plebanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:02:59 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Ascoli property for function
spaces and the weak topology of Banach and Fr\'echet spaces" by
S. Gabriyelyan, J. Kakol, and G. Plebanek.
Abstract:
Following [3] we say that a Tychonoff space $X$ is an Ascoli space
if every compact subset $\mathcal{K}$ of $C_k(X)$ is evenly continuous;
this notion is closely related to the classical Ascoli theorem. Every
$k_\mathbb{R}$-space, hence any $k$-space, is Ascoli.
Let $X$ be a metrizable space. We prove that the space $C_{k}(X)$
is Ascoli iff $C_{k}(X)$ is a $k_\mathbb{R}$-space iff $X$ is locally
compact. Moreover, $C_{k}(X)$ endowed with the weak topology is Ascoli
iff $X$ is countable and discrete.
Using some basic concepts from probability theory and measure-theoretic
properties of $\ell_1$, we show that the following assertions are
equivalent for a Banach space $E$: (i) $E$ does not contain isomorphic
copy of $\ell_1$, (ii) every real-valued sequentially continuous map
on the unit ball $B_{w}$ with the weak topology is continuous, (iii)
$B_{w}$ is a $k_\mathbb{R}$-space, (iv) $B_{w}$ is an Ascoli space.
We prove also that a Fr\'{e}chet lcs $F$ does not contain isomorphic
copy of $\ell_1$ iff each closed and convex bounded subset of $F$
is Ascoli in the weak topology. However we show that a Banach space
$E$ in the weak topology is Ascoli iff $E$ is finite-dimensional. We
supplement the last result by showing that a Fr\'{e}chet lcs $F$ which
is a quojection is Ascoli in the weak topology iff either $F$ is finite
dimensional or $F$ is isomorphic to the product $\mathbb{K}^{\mathbb{N}}$,
where $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46A04, 46B03, 54C30
Submitted from: saak at bgu.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.04202
or
http://arXiv.org/abs/1504.04202
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean Bourgain and Mark Lewko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:04:30 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Sidonicity and variants of
Kaczmarz's problem" by Jean Bourgain and Mark Lewko.
Abstract:
We prove that a uniformly bounded system of orthonormal functions
satisfying the $\psi_2$ condition: (1) must contain a Sidon subsystem
of proportional size, (2) must satisfy the Rademacher-Sidon property,
and (3) must have its 5-fold tensor satisfy the Sidon property. On the
other hand, we construct a uniformly bounded orthonormal system that
satisfies the $\psi_2$ condition but which is not Sidon. These problems
are variants of Kaczmarz's Scottish book problem (problem 130) which, in
its original formulation, was answered negatively by Rudin. A corollary
of our argument is a new, elementary proof of Pisier's theorem that a
set of characters satisfying the $\psi_2$ condition is Sidon.
Archive classification: math.CA math.FA math.PR
Remarks: 22 pages, no figures
Submitted from: mlewko at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.05290
or
http://arXiv.org/abs/1504.05290
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michal Doucha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:06:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An example of a non-commutative
uniform Banach group" by Michal Doucha.
Abstract:
We construct a non-commutative uniform Banach group which has the free
group of countably many generators as a dense subgroup.
Archive classification: math.FA math.GN math.GR
Submitted from: m.doucha at post.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.05841
or
http://arXiv.org/abs/1504.05841
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej Kurka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:08:25 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Amalgamations of classes of Banach
spaces with a monotone basis" by Ondrej Kurka.
Abstract:
It was proved by Argyros and Dodos that, for many classes $ C $
of separable Banach spaces which share some property $ P $, there exists
an isomorphically universal space that satisfies $ P $ as well. We
introduce a variant of their amalgamation technique which provides an
isometrically universal space in the case that $ C $ consists of spaces
with a monotone Schauder basis. For example, we prove that if $ C $
is a set of separable Banach spaces which is analytic with respect to
the Effros-Borel structure and every $ X \in C $ is reflexive and has a
monotone Schauder basis, then there exists a separable reflexive Banach
space that is isometrically universal for $ C $.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B15, 46B20,
46B70 (Secondary)
Submitted from: kurka.ondrej at seznam.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.06862
or
http://arXiv.org/abs/1504.06862
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Martin Bohata, Jan Hamhalter and Ondrej
F.K. Kalenda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:10:03 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On Markushevich bases in preduals
of von Neumann algebras" by Martin Bohata, Jan Hamhalter and Ondrej
F.K. Kalenda.
Abstract:
We prove that the predual of any von Neumann algebra is $1$-Plichko,
i.e., it has a countably $1$-norming Markushevich basis. This answers
a question of the third author who proved the same for preduals of
semifinite von Neumann algebras. As a corollary we obtain an easier
proof of a result of U.~Haagerup that the predual of any von Neumann
algebra enjoys the separable complementation property. We further prove
that the self-adjoint part of the predual is $1$-Plichko as well.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B26, 46L10
Remarks: 13 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/1504.06981
or
http://arXiv.org/abs/1504.06981
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Lancien, Antonin Prochazka, and
Matias Raja
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:11:24 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Szlenk indices of convex hulls"
by Gilles Lancien, Antonin Prochazka, and Matias Raja.
Abstract:
We study the general measures of non compactness defined on subsets of a
dual Banach space, their associated derivations and their
$\omega$-iterates. We introduce the notion of convexifiable measure
of non compactness and investigate the properties of its associated
fragment and slice derivations. We apply our results to the Kuratowski
measure of non compactness and to the study of the Szlenk index of a
Banach space. As a consequence, we obtain, for any countable ordinal
$\alpha$, a characterization of the Banach spaces with Szlenk index
bounded by $\omega^{\alpha+1}$ in terms of the existence an equivalent
renorming. This extends a result by Knaust, Odell and Schlumprecht on
Banach spaces with Szlenk index equal to $\omega$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.06997
or
http://arXiv.org/abs/1504.06997
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Triloki Nath
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 29 Apr 2015 15:12:39 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Differentiability of Distance
Function and The Proximinal Condition implying Convexity" by Triloki Nath.
Abstract:
A necessary and sufficient condition for the differentiability of the
distance function generated by an almost proximinal closed set has
been given for normed linear spaces with locally uniformly convex and
differentiable norm. We prove that the proximinal condition of Giles
[6] is true for almost sun. In such spaces if the proximinal condition
is satisfied and the distance function is uniformly differentiable on
a dense set then it turn in the differentiability on all off the set
(generating the distance function). The proximinal condition ensures
about the convexity of almost sun in some spaces under a differentiability
condition of the distance function. A necessary and sufficient condition
is derived for the convexity of Chebyshev sets in Banach spaces with
rotund dual.
Archive classification: math.FA
Mathematics Subject Classification: 41A65, 46B20
Remarks: 9 pages
Submitted from: tnath at dhsgsu.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.07292
or
http://arXiv.org/abs/1504.07292
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Liang Hong
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 18 May 2015 14:39:26 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the relationship between order
bounded operators, topologically bounded operators and topologically
continuous operators" by Liang Hong.
Abstract:
The relationship between order bounded operators and order continuous
operators has been investigated by several authors. The purpose of
this paper is to study the relationship between order bounded operators,
topologically bounded operators and topologically continuous operators. We
give conditions for (i) the space of topologically continuous operators
to be an ideal of the space of order bounded operators; this result
generalizes the Nakano-Roberts Theorem; (ii) the space of topologically
continuous operators to be a band of the space of order bounded operators;
(iii) the space of order bounded operators to coincide with the space of
topologically bounded operators; (iv) the space of order bounded operators
to coincide with the space of topologically continuous operators. In
addition, a set of counterexamples are given for illustration purpose;
these counterexamples are interesting in their own rights and contribute
to the literature.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B60, 47B65, Secondary 46A40,
06B30, 06F30
Submitted from: hong at rmu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.08016
or
http://arXiv.org/abs/1504.08016
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros, Ioannis Gasparis and
Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 18 May 2015 14:41:03 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the structure of separable
$\mathcal{L}_\infty$-spaces" by Spiros A. Argyros, Ioannis Gasparis and
Pavlos Motakis.
Abstract:
Based on a construction method introduced by J. Bourgain and F. Delbaen,
we give a general definition of a Bourgain-Delbaen space and prove
that every infinite dimensional separable $\mathcal{L}_\infty$-space
is isomorphic to such a space. Furthermore, we provide an example of a
$\mathcal{L}_\infty$ and asymptotic $c_0$ space not containing $c_0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B07
Remarks: 15 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/1504.08223
or
http://arXiv.org/abs/1504.08223
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tony K. Nogueira and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 18 May 2015 14:42:31 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the size of certain subsets
of invariant Banach sequence spaces" by Tony K. Nogueira and Daniel
Pellegrino.
Abstract:
In this note we improve some recent results of G. Botelho and V.
F\'{a}varo on invariant Banach sequence spaces. Our main result shows
that, under very weak assumptions, more general versions of some subsets
of invariant sequence spaces investigated by G. Botelho and V. F\'{a}varo
in 2014 contain, up to the null vector, a closed infinite-dimensional
subspace .
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/1504.08238
or
http://arXiv.org/abs/1504.08238
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Lorenzo Cavallina
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 18 May 2015 14:44:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Non-trivial translation-invariant
valuations on $L^\infty$" by Lorenzo Cavallina.
Abstract:
Translation-invariant valuations on the space $L^\infty(\mathbb{R}^n)$
are examined. We prove that such functionals vanish on functions
with compact support. Moreover a rich family of non-trivial
translation-invariant valuations on $L^\infty(\mathbb{R}^n)$ is
constructed through the use of ultrafilters on $\mathbb{R}$.
Archive classification: math.FA
Mathematics Subject Classification: 46E30 (52B45)
Remarks: 23 pages, 2 figures
Submitted from: cava at ims.is.tohoku.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.00089
or
http://arXiv.org/abs/1505.00089
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jussi Laitila and Hans-Olav Tylli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 18 May 2015 14:45:38 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Composition operators on
vector-valued analytic function spaces: a survey" by Jussi Laitila and
Hans-Olav Tylli.
Abstract:
We survey recent results about composition operators induced by analytic
self-maps of the unit disk in the complex plane on various Banach
spaces of analytic functions taking values in infinite-dimensional
Banach spaces. We mostly concentrate on the research line into
qualitative properties such as weak compactness, initiated by Liu,
Saksman and Tylli (1998), and continued in several other papers. We
discuss composition operators on strong, respectively weak, spaces of
vector-valued analytic functions, as well as between weak and strong
spaces. As concrete examples, we review more carefully and present some
new observations in the cases of vector-valued Hardy and BMOA spaces,
though the study of composition operators has been extended to a wide
range of spaces of vector-valued analytic functions, including spaces
defined on other domains. Several open problems are stated.
Archive classification: math.FA
Mathematics Subject Classification: 47B33, 46E15, 46E40, 47B07
Citation: Acta et Commentationes Universitatis Tartuensis de Mathematica
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.01945
or
http://arXiv.org/abs/1505.01945
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:03:14 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An isometrically universal Banach
space induced by a non-universal Boolean algebra" by Christina Brech
and Piotr Koszmider.
Abstract:
Given a Boolean algebra $A$, we construct another Boolean algebra $B$
with no uncountable well-ordered chains such that the Banach space of
real valued continuous functions $C(K_A)$ embeds isometrically into
$C(K_B)$, where $K_A$ and $K_B$ are the Stone spaces of $A$ and $B$
respectively. As a consequence we obtain the following: If there exists
an isometrically universal Banach space for the class of Banach spaces
of a given uncountable density $\kappa$, then there is another such space
which is induced by a Boolean algebra which is not universal for Boolean
algebras of cardinality $\kappa$. Such a phenomenon cannot happen on the
level of separable Banach spaces and countable Boolean algebras. This
is related to the open question if the existence of an isometrically
universal Banach space and of a universal Boolean algebra are equivalent
on the nonseparable level (both are true on the separable level).
Archive classification: math.FA math.GN math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.04776
or
http://arXiv.org/abs/1505.04776
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio M. Peralta and Hermann Pfitzner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:04:56 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Weak Banach-Saks property and
Koml\'os' theorem for preduals of JBW$^*$-triples" by Antonio M. Peralta
and Hermann Pfitzner.
Abstract:
We show that the predual of a JBW$^*$-triple has the weak Banach-Saks
property, that is, reflexive subspaces of a JBW$^*$-triple predual are
super-reflexive. We also prove that JBW$^*$-triple preduals satisfy
the Koml\'os property (which can be considered an abstract version of
the weak law of large numbers). The results rely on two previous papers
from which we infer the fact that, like in the classical case of $L^1$,
a subspace of a JBW$^*$-triple predual contains $\ell_1$ as soon as it
contains uniform copies of $\ell_1^n$.
Archive classification: math.OA math.FA
Submitted from: aperalta at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.05302
or
http://arXiv.org/abs/1505.05302
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Henning Kempka and Jan Vybiral
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:07:09 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Volumes of unit balls of mixed
sequence spaces" by Henning Kempka and Jan Vybiral.
Abstract:
The volume of the unit ball of the Lebesgue sequence space $\ell_p^m$
is very well known since the times of Dirichlet. We calculate the volume
of the unit ball in the mixed norm $\ell^n_q(\ell_p^m)$, whose special
cases are nowadays popular in machine learning under the name of group
lasso. We consider the real as well as the complex case. The result is
given by a closed formula involving the gamma function, only slightly
more complicated than the one of Dirichlet. We close by an overview of
open problems.
Archive classification: math.FA
Submitted from: vybiral at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.05867
or
http://arXiv.org/abs/1505.05867
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by E. Ostrovsky and L. Sirota
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:09:46 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Strengthening of weak convergence
for Radon measures in separable Banach spaces" by E. Ostrovsky and
L. Sirota.
Abstract:
We prove in this short report that for arbitrary weak converging
sequence of sigma-finite Borelian measures in the separable Banach space
there is a compact embedded separable subspace such that this measures
not only are concentrated in this subspace but weak converge therein.
Archive classification: math.FA
Submitted from: leos at post.sce.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1505.06235
or
http://arXiv.org/abs/1505.06235
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: Thu, 11 Jun 2015 15:11:17 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Nontrivial twisted sums of $c_0$
and $C(K)$" by Claudia Correa and Daniel V. Tausk.
Abstract:
We obtain a new large class of compact Hausdorff spaces $K$ for
which $c_0$ can be nontrivially twisted with $C(K)$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E15
Remarks: 10 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/1505.06727
or
http://arXiv.org/abs/1505.06727
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth, Michal Doucha, and Przemyslaw
Wojtaszczyk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:12:51 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the structure of Lipschitz-free
spaces" by Marek Cuth, Michal Doucha, and Przemyslaw Wojtaszczyk.
Abstract:
In this note we study the structure of Lipschitz-free Banach spaces. We
show that every Lipschitz-free Banach space contains a complemented
copy of $\ell_1$. This result has many consequences for the structure of
Lipschitz-free Banach spaces. Moreover, we give an example of a countable
compact metric space $K$ such that $F(K)$ is not isomorphic to a subspace
of $L_1$ and we show that whenever $M$ is a subset of $R^n$, then $F(M)$
is weakly sequentially complete; in particular, $c_0$ does not embed
into $F(M)$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 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/1505.07209
or
http://arXiv.org/abs/1505.07209
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth and Marian Fabian
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:14:15 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Separable reduction of Frechet
subdifferentiability in Asplund spaces" by Marek Cuth and Marian Fabian.
Abstract:
In the framework of Asplund spaces, we use two equivalent instruments -
rich families and suitable models from logic - for performing separable
reductions of various statements on Frechet subdifferentiability
of functions. This way, isometrical results are actually obtained and
several existed proofs are substantially simplified. Everything is based
on a new structural characterization of Asplund spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 58C20, 46B20, 03C30
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/1505.07604
or
http://arXiv.org/abs/1505.07604
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pablo Turco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:15:38 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "$\mathcal A$-compact mappings"
by Pablo Turco.
Abstract:
For a fixed Banach operator ideal $\mathcal A$, we study $\mathcal
A$-compact polynomials and $\mathcal A$-compact holomorphic mappings. We
show that the behavior of $\mathcal A$-compact polynomials is determined
by its behavior in any neighborhood of any point. We transfer some known
properties of $\mathcal A$-compact operators to $\mathcal A$-compact
polynomials. In order to study $\mathcal A$-compact holomorphic functions,
we appeal to the $\mathcal A$-compact radius of convergence which
allows us to characterize the functions in this class. Under certain
hypothesis on the ideal $\mathcal A$, we give examples showing that our
characterization is sharp.
Archive classification: math.FA
Mathematics Subject Classification: 46G20, 46B20, 46G25
Remarks: 21 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/1505.08037
or
http://arXiv.org/abs/1505.08037
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by J. L. Ansorena, F. Albiac, S. J. Dilworth
and Denka Kutzarova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:16:52 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Existence and uniqueness of greedy
bases in Banach spaces" by J. L. Ansorena, F. Albiac, S. J. Dilworth
and Denka Kutzarova.
Abstract:
Our aim is to investigate the properties of existence and uniqueness of
greedy bases in Banach spaces. We show the non-existence of greedy
basis in some Nakano spaces and Orlicz sequence spaces and produce the
first-known examples of non-trivial spaces (i.e., different from $c_0$,
$\ell_1$, and $\ell_2$) with a unique greedy basis.
Archive classification: math.FA
Mathematics Subject Classification: 46B15 (Primary) 46B45 (Secondary)
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/1505.08119
or
http://arXiv.org/abs/1505.08119
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Y. Estaremi, S. Maghsodi and I. Rahmani
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:18:18 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "on properties of multiplication
and composition operators between spaces" by Y. Estaremi, S. Maghsodi
and I. Rahmani.
Abstract:
In this paper, we study bounded and closed range multiplication and
composition operators between two different Orlicz spaces.
Archive classification: math.FA
Remarks: 22 pages
Submitted from: estaremi at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.00369
or
http://arXiv.org/abs/1506.00369
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: Thu, 11 Jun 2015 15:19:47 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A Valdivia compact space with no
$G_\delta$ points and few nontrivial convergent sequences" by Claudia
Correa and Daniel V. Tausk.
Abstract:
We give an example of a Valdivia compact space with no $G_\delta$
points and no nontrivial convergent sequences in the complement of a
dense $\Sigma$-subset. The example is related to a problem concerning
twisted sums of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 54D30, 54F05, 46B20, 46E15
Remarks: 3 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/1506.02077
or
http://arXiv.org/abs/1506.02077
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Apoorva Khare and Bala Rajaratnam
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:21:11 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Probability inequalities and tail
estimates on metric semigroups" by Apoorva Khare and Bala Rajaratnam.
Abstract:
The goal of this work is to study probability inequalities leading
to tail estimates in a general metric semigroup $\mathscr{G}$ with a
translation-invariant metric $d_{\mathscr{G}}$. We begin by proving
inequalities including those by Ottaviani-Skorohod, L\'evy, Mogul'skii,
and Khinchin-Kahane in arbitrary semigroups $\mathscr{G}$. We then
show a variant of Hoffmann-J{\o}rgensen's inequality, which unifies
and significantly strengthens several versions in the Banach space
literature, including those by Johnson and Schechtman [Ann. Prob. 17],
Klass and Nowicki [Ann. Prob. 28], and Hitczenko and Montgomery-Smith
[Ann. Prob. 29]. Moreover, our version of the inequality holds more
generally, in the minimal mathematical framework of a metric semigroup
$\mathscr{G}$. This inequality has important consequences (as in the
Banach space literature) in obtaining tail estimates and approximate
bounds for sums of independent semigroup-valued random variables, their
moments, and decreasing rearrangements. In particular, we obtain the
"correct" universal constants in several cases, including in all normed
linear spaces as well as in all compact, discrete, or abelian Lie groups.
Archive classification: math.PR math.FA math.GR
Mathematics Subject Classification: 60B15
Remarks: 32 pages, LaTeX
Submitted from: khare at stanford.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.02605
or
http://arXiv.org/abs/1506.02605
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Umut Caglar and Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:22:40 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Orlicz Affine Isoperimetric
Inequalities for Functions" by Umut Caglar and Deping Ye.
Abstract:
In this paper, we develop basic theory for the Orlicz affine surface
areas for log-concave and $s$-concave functions. Our definitions were
motivated by recently developed 1) Orlicz affine and geominimal surface
areas for convex bodies, and 2) $L_p$ affine surface areas for log-concave
and $s$-concave functions. We prove some basic properties for these
newly introduced functional affine invariants, and establish related
functional affine isoperimetric inequalities as well as generalized
functional Blaschke-Santal\'o and inverse Santal\'o inequalities.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20, 53A15, 46B, 60B
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/1506.02974
or
http://arXiv.org/abs/1506.02974
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by F. Albiac and J. L. Ansorena
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 11 Jun 2015 15:24:06 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Characterization of $1$-almost
greedy bases" by F. Albiac and J. L. Ansorena.
Abstract:
This article closes the cycle of characterizations of greedy-like
bases in the isometric case initiated in [F. Albiac and P. Wojtaszczyk,
Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006)]
with the characterization of $1$-greedy bases and continued in
[F. Albiac and J. L. Ansorena, Characterization of $1$-quasi-greedy
bases, arXiv:1504.04368v1 [math.FA] (2015)] with the characterization
of $1$-quasi-greedy bases. Here we settle the problem of providing a
characterization of $1$-almost greedy bases in (real or complex) Banach
spaces. We show that a (semi-normalized) basis in a Banach space is
almost-greedy with almost greedy constant equal to $1$ if and only if
it is quasi-greedy with suppression quasi-greedy constant equal to $1$
and has Property (A).
Archive classification: math.FA
Mathematics Subject Classification: 46B15 (Primary) 41A65, 46B15
(Secondary)
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/1506.03397
or
http://arXiv.org/abs/1506.03397
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS 2015
Date: Fri, 26 Jun 2015 14:07:38 -0500
From: Bill Johnson <johnson at math.tamu.edu>
To: <banach at mathdept.okstate.edu>
1st ANNOUNCEMENT OF SUMIRFAS 2015
The Summer Informal Regional Functional Analysis Seminar
July 31 - August 2
Texas A&M University, College Station
The speakers for SUMIRFAS 2015 are
Natasha Blitvic Laszlo Lempert
Bernhard Bodmann Laurent Marcoux
Alperen Ergur Rishika Rupam
Bill Helton Nikhil Srivastava
Mehrdad Kalantar Sheng Zhang
The SUMIRFAS 2015 homepage can be found at
http://www.math.tamu.edu/~kerr/workshop/sumirfas2015
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 the break room on the first
floor of Blocker.
SUMIRFAS will be preceded from July 27 to 31 by the Concentration Week
"From
Commutators to BCP Operators", organized by Hari Bercovici and Vern
Paulsen. The meeting will focus on the areas of mathematics developed by
Carl Pearcy, who is turning 80 this year, and aims to promote connections
between several different themes in operator theory which have been
driving recent progress in the subject. Topics will include
quasidiagonality,
commutators of operators, and invariant subspaces. The homepage of the
Concentration Week is located at
http://www.math.tamu.edu/~kerr/concweek15
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 "From Commutators to
BCP Operators", please contact Hari Bercovici <bercovic at indiana.edu>
or Vern Paulsen <vern at math.uh.edu>.
_______________________________________________
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 Van Hoang Nguyen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:33:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Improved $L_p-$mixed volume
inequality for convex bodies" by Van Hoang Nguyen.
Abstract:
A sharp quantitative version of the $L_p-$mixed volume inequality is
established. This is achieved by exploiting an improved
Jensen inequality. This inequality is a generalization of
Pinsker-Csisz\'ar-Kullback inequality for the Tsallis entropy. Finally,
a sharp quantitative version of the $L_p-$Brunn-Minkowski inequality is
also proved as a corollary.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 26D15, 52A20, 52A39, 52A40
Remarks: 11 pages, to appear in J. Math. Anal. Appl
Submitted from: vanhoang0610 at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.04250
or
http://arXiv.org/abs/1506.04250
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor and Yuval Rabani
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:34:22 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On Lipschitz extension from finite
subsets" by Assaf Naor and Yuval Rabani.
Abstract:
We prove that for every $n\in \mathbb{N}$ there exists a metric space
$(X,d_X)$, an $n$-point subset $S\subseteq X$, a Banach space
$(Z,\|\cdot\|_Z)$ and a $1$-Lipschitz function $f:S\to Z$ such that
the Lipschitz constant of every function $F:X\to Z$ that extends $f$
is at least a constant multiple of $\sqrt{\log n}$. This improves
a bound of Johnson and Lindenstrauss. We also obtain the following
quantitative counterpart to a classical extension theorem of Minty. For
every $\alpha\in (1/2,1]$ and $n\in \mathbb{N}$ there exists a
metric space $(X,d_X)$, an $n$-point subset $S\subseteq X$ and a
function $f:S\to \ell_2$ that is $\alpha$-H\"older with constant
$1$, yet the $\alpha$-H\"older constant of any $F:X\to \ell_2$
that extends $f$ satisfies $$ \|F\|_{\mathrm{Lip}(\alpha)}\gtrsim
(\log n)^{\frac{2\alpha-1}{4\alpha}}+\left(\frac{\log n}{\log\log
n}\right)^{\alpha^2-\frac12}. $$ We formulate a conjecture whose positive
solution would strengthen Ball's nonlinear Maurey extension theorem,
serving as a far-reaching nonlinear version of a theorem of K\"onig,
Retherford and Tomczak-Jaegermann. We explain how this conjecture would
imply as special cases answers to longstanding open questions of Johnson
and Lindenstrauss and Kalton.
Archive classification: math.MG math.FA
Submitted from: naor at math.princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.04398
or
http://arXiv.org/abs/1506.04398
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond A. Abrahamsen, Peter Hajek, Olav
Nygaard, Jarno Talponen, and Stanimir Troyanski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:39:36 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Diameter 2 properties and
convexity" by Trond A. Abrahamsen, Peter Hajek, Olav Nygaard, Jarno
Talponen, and Stanimir Troyanski.
Abstract:
We present an equivalent midpoint locally uniformly rotund (MLUR)
renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$
satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator
on $X$). As a consequence we obtain an MLUR space $X$ with the properties
D2P, that every non-empty relatively weakly open subset of its unit ball
$B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and
every norm 1 element $x$ inside the slice there is another element $y$
inside the slice of distance as close to 2 from $x$ as desired. An example
of an MLUR space with the D2P, the LD2P+, and with convex combinations
of slices of arbitrary small diameter is also given.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20
Remarks: 15 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/1506.05237
or
http://arXiv.org/abs/1506.05237
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:41:19 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Uniform nonextendability from nets"
by Assaf Naor.
Abstract:
It is shown that there exist Banach spaces $X,Y$, a $1$-net
$\mathscr{N}$ of $X$ and a Lipschitz function $f:\mathscr{N}\to Y$
such that every $F:X\to Y$ that extends $f$ is not uniformly continuous.
Archive classification: math.MG math.FA
Submitted from: naor at math.princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.05391
or
http://arXiv.org/abs/1506.05391
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean Bourgain
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:42:26 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On uniformly bounded basis in
spaces of holomorphic functions" by Jean Bourgain.
Abstract:
The main result of the paper is the construction of explicit uniformly
bounded basis in the spaces of complex homogenous polynomials on the unit
ball of $C^3$, extending an earlier result of the author in the $C^2$ case
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46E15, 32A99 Secondary: 42A56
Submitted from: bourgain at ias.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.05694
or
http://arXiv.org/abs/1506.05694
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jarno Talponen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:43:55 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Point-open games and productivity
of dense-separable property" by Jarno Talponen.
Abstract:
In this note we study the point-open topological games to analyze
the least upper bound for density of dense subsets of a topological
space. This way we may also analyze the behavior of such cardinal
invariants in taking products of spaces. Various related cardinal
equalities and inequalities are given. As an application we take a
look at Banach spaces with the property (CSP) which can be formulated
by stating that each weak-star dense linear subspace of the dual is
weak-star separable.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54A25, 54D70, 91A44, 46B26, 03E60
Submitted from: talponen at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.06080
or
http://arXiv.org/abs/1506.06080
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by E. Dahia, D. Achour, P. Rueda and E. A.
Sanchez Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:46:30 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Domination spaces and factorization
of linear and multilinear summing operators" by E. Dahia, D. Achour,
P. Rueda and E. A. Sanchez Perez.
Abstract:
It is well known that not every summability property for non linear
operators leads to a factorization theorem. In this paper we undertake a
detailed study of factorization schemes for summing linear and nonlinear
operators. Our aim is to integrate under the same theory a wide family
of classes of mappings for which a Pietsch type factorization theorem
holds. We analyze the class of linear operators that are defined by a
summability inequality involving a homogeneous map. Our construction
includes the cases of absolutely $p$-summing linear operators,
$(p,\sigma)$-absolutely continuous linear operators, factorable
strongly $p$-summing multilinear operators, $(p_1,\ldots,p_n)$-dominated
multilinear operators and dominated $(p_1,\ldots, p_n;\sigma)$-continuous
multilinear operators.
Archive classification: math.FA
Submitted from: hajdahia at univ-msila.dz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.06311
or
http://arXiv.org/abs/1506.06311
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergei V. Astashkin and Lech Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:47:52 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Rademacher functions in Morrey
spaces" by Sergei V. Astashkin and Lech Maligranda.
Abstract:
The Rademacher functions are investigated in the Morrey spaces M(p,w) on
[0,1] for 1 \le p <\infty and weight w being a quasi-concave
function. They span l_2 space in M(p,w) if and only if the weight w is
smaller than the function log_2^{-1/2}(2/t) on (0,1). Moreover, if 1 <
p < \infty the Rademacher sunspace R_p is complemented in M(p,w) if and
only if it is isomorphic to l_2. However, the Rademacher subspace is
not complemented in M(1,w) for any quasi-concave weight w. In the last
part of the paper geometric structure of Rademacher subspaces in Morrey
spaces M(p,w) is described. It turns out that for any infinite-dimensional
subspace X of R_p the following alternative holds: either X is isomorphic
to l_2 or X contains a subspace which is isomorphic to c_0 and is
complemented in R_p.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42
Remarks: 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/1506.06862
or
http://arXiv.org/abs/1506.06862
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Istvan Berkes and Robert Tichy
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:49:08 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Kadec-Pe\l czynski theorem
in $L^p$, $1\le p<2$" by Istvan Berkes and Robert Tichy.
Abstract:
By a classical result of Kadec and Pe\l czynski (1962), every normalized
weakly null sequence in $L^p$, $p>2$ contains a subsequence equivalent
to the unit vector basis of $\ell^2$ or to the unit vector basis of
$\ell^p$. In this paper we investigate the case $1\le p<2$ and show
that a necessary and sufficient condition for the first alternative in
the Kadec-Pe\l czynski theorem is that the limit random measure $\mu$
of the sequence satisfies $\int_{\mathbb{R}} x^2 d\mu (x)\in L^{p/2}$.
Archive classification: math.FA
Submitted from: berkes at tugraz.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.07453
or
http://arXiv.org/abs/1506.07453
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Arne Roggensack
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:50:16 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A short note on the Radon-Riesz
property for continuous Banach space valued functions" by Arne
Roggensack.
Abstract:
We present a generalization of the Radon-Riesz property to sequences of
continuous functions with values in uniformly convex and uniformly smooth
Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46B50, Secondary: 46B20
Submitted from: arne.roggensack at wias-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.07682
or
http://arXiv.org/abs/1506.07682
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephen J. Dilworth, Denka Kutzarova,
Gilles Lancien and Lovasoa N. Randrianarivony
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:51:32 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Equivalent norms with the property
$(\beta)$ of Rolewicz" by Stephen J. Dilworth, Denka Kutzarova, Gilles
Lancien and Lovasoa N. Randrianarivony.
Abstract:
We extend to the non separable setting many characterizations of the
Banach spaces admitting an equivalent norm with the property $(\beta)$
of Rolewicz. These characterizations involve in particular the Szlenk
index and asymptotically uniformly smooth or convex norms. This allows
to extend easily to the non separable case some recent results from the
non linear geometry of Banach spaces.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1506.07978
or
http://arXiv.org/abs/1506.07978
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark Veraar and Lutz Weis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 29 Jun 2015 12:52:56 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Estimates for vector-valued
holomorphic functions and Littlewood-Paley-Stein theory" by Mark Veraar
and Lutz Weis.
Abstract:
In this paper we consider generalized square function norms of
holomorphic functions with values in a Banach space. One of the main
results is a characterization of embeddings of the form \[L^p(X)\subseteq
\gamma(X) \subseteq L^q(X),\] in terms of the type $p$ and cotype $q$
for the Banach space $X$. As an application we prove $L^p$-estimates
for vector-valued Littlewood-Paley-Stein $g$-functions and derive an
embedding result for real and complex interpolation spaces under type
and cotype conditions.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B09, Secondary: 42B25,
46B70, 46E40, 46B20, 47D07
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/1506.08013
or
http://arXiv.org/abs/1506.08013
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuele Casini, Enrico Miglierina, and
Lukasz Piasecki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:02:15 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Rethinking Polyhedrality for
Lindenstrauss Spaces" by Emanuele Casini, Enrico Miglierina, and Lukasz
Piasecki.
Abstract:
A recent example by the authors (see arXiv:1503.09088 [math.FA]) shows
that an old result of Zippin about the existence of an isometric copy of
$c$ in a separable Lindenstrauss space is incorrect. The same example
proves that some characterizations of polyhedral Lindenstrauss spaces,
based on the result of Zippin, are false. The main result of the present
paper provides a new characterization of polyhedrality for the preduals
of $\ell_{1}$ and gives a correct proof for one of the older. Indeed,
we prove that for a space $X$ such that $X^{*}=\ell_{1}$ the following
properties are equivalent:
(1) $X$ is a polyhedral space; (2) $X$ does not contain an isometric
copy of $c$; (3) $\sup\left\{ x^{*}(x)\,:\,
x^{*}\in\mathrm{ext}\left(B_{X^{*}}\right)\setminus D(x)\right\}
<1$ for each $x\in S_{X}$, where $D(x)=\left\{ x^{*}\in
S_{X^{*}}:x^{*}(x)=1\right\}$.
By known theory, from our result follows that a generic Lindenstrauss
space is polyhedral if and only if it does not contain an isometric copy
of $c$. Moreover, a correct version of the result of Zippin is derived
as a corollary of the main result.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20, 46B25
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/1506.08559
or
http://arXiv.org/abs/1506.08559
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by O. Delgado and E. A. Sanchez Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:04:30 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Strong extensions for $q$-summing
operators acting in $p$-convex function spaces for $1 \le p \le q$"
by O. Delgado and E. A. Sanchez Perez.
Abstract:
Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function
space over a $\sigma$-finite measure $\mu$. We combine the structure
of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space
$S_{X_p}^{\,q}(\xi)$, where $\xi$ is a probability Radon measure on a
certain compact set associated to $X$. We show some of its properties,
and the relevant fact that every $q$-summing operator $T$ defined on $X$
can be continuously (strongly) extended to $S_{X_p}^{\,q}(\xi)$. This
result turns out to be a mixture of the Pietsch and Maurey-Rosenthal
factorization theorems, which provide (strong) factorizations for
$q$-summing operators through $L^q$-spaces when $1 \le q \le p$. Thus, our
result completes the picture, showing what happens in the complementary
case $1\le p\le q$, opening the door to the study of the multilinear
versions of $q$-summing operators also in these cases.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 47B38
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/1506.09010
or
http://arXiv.org/abs/1506.09010
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ivan Soprunov and Artem Zvavitch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:06:07 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Bezout Inequality for Mixed
volumes" by Ivan Soprunov and Artem Zvavitch.
Abstract:
In this paper we consider the following analog of Bezout inequality
for mixed volumes: $$V(P_1,\dots,P_r,\Delta^{n-r})V_n(\Delta)^{r-1}\leq
\prod_{i=1}^r V(P_i,\Delta^{n-1})\ \text{ for }2\leq r\leq n.$$ We show
that the above inequality is true when $\Delta$ is an $n$-dimensional
simplex and $P_1, \dots, P_r$ are convex bodies in $\mathbb{R}^n$. We
conjecture that if the above inequality is true for all convex bodies
$P_1, \dots, P_r$, then $\Delta$ must be an $n$-dimensional simplex. We
prove that if the above inequality is true for all convex bodies
$P_1, \dots, P_r$, then $\Delta$ must be indecomposable (i.e. cannot
be written as the Minkowski sum of two convex bodies which are not
homothetic to $\Delta$), which confirms the conjecture when $\Delta$
is a simple polytope and in the 2-dimensional case. Finally, we connect
the inequality to an inequality on the volume of orthogonal projections
of convex bodies as well as prove an isomorphic version of the inequality.
Archive classification: math.MG math.FA
Mathematics Subject Classification: Primary 52A39, 52B11, 52A20,
Secondary 52A23
Remarks: 18 pages, 2 figures
Submitted from: i.soprunov at csuohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.00765
or
http://arXiv.org/abs/1507.00765
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manaf Adnan Saleh Saleh
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:09:29 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Nonlinear Operator Ideals Between
Metric Spaces and Banach Spaces, Part I" by Manaf Adnan Saleh Saleh.
Abstract:
In this paper we present part I of nonlinear operator ideals theory
between metric spaces and Banach spaces. Building upon the definition
of operator ideal between arbitrary Banach spaces of A. Pietsch we pose
three types of nonlinear versions of operator ideals. We introduce several
examples of nonlinear ideals and the relationships between them. For every
space ideal $\mathsf{A}$ can be generated by a special nonlinear ideal
which consists of those Lipschitz operators admitting a factorization
through a Banach space $\mathbf{M}\in\mathsf{A}$. We investigate products
and quotients of nonlinear ideals. We devote to constructions three types
of new nonlinear ideals from given ones. A ``new'' is a rule defining
nonlinear ideals $\mathfrak{A}^{L}_{new}$, $\textswab{A}^{L}_{new}$, and
$\textfrak{A}^{L}_{new}$ for every $\mathfrak{A}$, $\textswab{A}^{L}$,
and $\textfrak{A}^{L}$ respectively, are called a Lipschitz procedure.
Considering the class of all stable objects for a given Lipschitz
procedure we obtain nonlinear ideals having special properties. We
present the concept of a (strongly) $p-$Banach nonlinear ideal ($0<p<1$)
and prove that the nonlinear ideals of Lipschitz nuclear operators,
Lipschitz Hilbert operators, products and quotient are strongly $r-$Banach
nonlinear ideals ($0<r<1$).
Archive classification: math.FA
Mathematics Subject Classification: 47Bxx, 46B28
Submitted from: manaf-adnan.saleh at uni-jena.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.00861
or
http://arXiv.org/abs/1507.00861
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:12:01 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Ideal structure of the algebra
of bounded operators acting on a Banach space" by Tomasz Kania and Niels
Jakob Laustsen.
Abstract:
We construct a Banach space $Z$ such that the lattice of closed
two-sided ideals of the Banach algebra $\mathscr{B}(Z)$
of bounded operators on $Z$ is as follows: $$ \{0\}\subset
\mathscr{K}(Z)\subset\mathscr{E}(Z)
\raisebox{-.5ex}%
{\ensuremath{\overset{\begin{turn}{30}$\subset$\end{turn}}%
{\begin{turn}{-30}$\subset$\end{turn}}}}\!\!%
\begin{array}{c}\mathscr{M}_1\\[1mm]\mathscr{M}_2\end{array}\!\!\!%
\raisebox{-1.25ex}%
{\ensuremath{\overset{\raisebox{1.25ex}{\ensuremath{\begin{turn}{-30}$\subset$\end{turn}}}}%
{\raisebox{-.25ex}{\ensuremath{\begin{turn}{30}$\subset$\end{turn}}}}}}\,\mathscr{B}(Z).
$$
We then determine which kinds of approximate identities
(bounded/left/right), if any, each of the four non-trivial closed
ideals of $\mathscr{B}(Z)$ contain, and we show that the maximal ideal
$\mathscr{M}_1$ is generated as a left ideal by two operators, but
not by a single operator, thus answering a question left open in our
collaboration with Dales, Kochanek and Koszmider (\emph{Studia Math.}
2013). In contrast, the other maximal ideal $\mathscr{M}_2$ is not
finitely generated as a left ideal.
The Banach space $Z$ is the direct sum of Argyros and Haydon's
Banach space $X_{\text{AH}}$ which has very few operators and a certain
subspace $Y$ of $X_{\text{AH}}$. The key property of~$Y$ is that every
bounded operator from $Y$ into $X_{\text{AH}}$ is the sum of a scalar
multiple of the inclusion mapping and a compact operator.
Archive classification: math.FA math.RA
Remarks: 21 pp
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/1507.01213
or
http://arXiv.org/abs/1507.01213
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andreas Seeger and Tino Ullrich
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:13:42 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Haar projection numbers and failure
of unconditional convergence in Sobolev spaces" by Andreas Seeger and
Tino Ullrich.
Abstract:
For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev
spaces for which the Haar system is an unconditional basis. We also
consider the natural extensions to Triebel-Lizorkin spaces and prove
upper and lower bounds for norms of projection operators depending on
properties of the Haar frequency set.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 46E35, 46B15, 42C40
Submitted from: seeger at math.wisc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.01211
or
http://arXiv.org/abs/1507.01211
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan M Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:15:10 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An alternate description of the
Szlenk index with applications" by Ryan M Causey.
Abstract:
We discuss an alternate method for computing the Szlenk index of an
arbitrary $w^*$ compact subsets of the dual of a Banach space. We discuss
consequences of this method as well as offer simple, alternative proofs
of a number of results already found in the literature.
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/1507.01993
or
http://arXiv.org/abs/1507.01993
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mohammed Bachir and Joel Blot
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 9 Jul 2015 15:17:04 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A useful lemma for Lagrange
multiplier rules in infinite dimension" by Mohammed Bachir and Joel Blot.
Abstract:
We give some reasonable and usable conditions on a sequence of norm one
in a dual banach space under which the sequence does not converges to the
origin in the $w^*$-topology. These requirements help to ensure that the
Lagrange multipliers are nontrivial, when we are interested for example
on the infinite dimensional infinite-horizon Pontryagin Principles for
discrete-time problems.
Archive classification: math.FA
Submitted from: mohammed.bachir at univ-paris1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.01919
or
http://arXiv.org/abs/1507.01919
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Damian Pinasco and Jorge
Tomas Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 13:19:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Non-linear Plank Problems and
polynomial inequalities" by Daniel Carando, Damian Pinasco and Jorge
Tomas Rodriguez.
Abstract:
In this article we study plank type problems for polynomials on
a Banach space $X$. Our aim is to find sufficient conditions on the
positive real numbers $a_1, \ldots, a_n,$ such that for continuous
polynomials $P_1,\ldots,P_n:X\rightarrow \mathbb C$ of degrees
$k_1,\ldots,k_n$, there exists a norm one element $\textbf{z}\in X$ for
which $|P_i(\textbf{z})| \ge a_i^{k_i}$ for $i=1,\ldots,n.$ In order to
do this, we prove some new inequalities for the norm of the product of
polynomials, which are of an independent interest.
Archive classification: math.FA
Remarks: 18 pages
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/1507.02316
or
http://arXiv.org/abs/1507.02316
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Petr Hajek, Gilles Lancien and Eva Pernecka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 13:21:24 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Lipschitz-free spaces over metric
spaces homeomorphic to the Cantor space" by Petr Hajek, Gilles Lancien
and Eva Pernecka.
Abstract:
In this note we give an example of a compact metric space which is
homeomorphic to the Cantor space and whose Lipschitz-free space fails
the approximation property. This answers a question by G. Godefroy. We
also prove that there exists an uncountable family of topologically
equivalent distances on the Cantor space whose free spaces are pairwise
non isomorphic.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.02701
or
http://arXiv.org/abs/1507.02701
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denny H. Leung and Wee-Kee Tang
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 13:22:47 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Persistence of Banach lattices
under nonlinear order isomorphisms" by Denny H. Leung and Wee-Kee Tang.
Abstract:
Ordered vector spaces E and F are said to be order isomorphic if
there is a (not necessarily linear) bijection between them that preserves
order. We investigate some situations under which an order isomorphism
between two Banach lattices implies the persistence of some linear
lattice structure. For instance, it is shown that if a Banach lattice E
is order isomorphic to C(K) for some compact Hausdorff space K, then E is
(linearly) isomorphic to C(K) as a Banach lattice. Similar results hold
for Banach lattices order isomorphic to c_0, and for Banach lattices
that contain a closed sublattice order isomorphic to c_0.
Archive classification: math.FA
Mathematics Subject Classification: 46B42
Submitted from: weekeetang at ntu.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.02759
or
http://arXiv.org/abs/1507.02759
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by P. Rueda and E.A. Sanchez-Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 13:24:18 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Dvoretsky-Rogers Theorem
for vector valued integrals on function spaces" by P. Rueda and
E.A. Sanchez-Perez.
Abstract:
We show a Dvoretsky-Rogers type Theorem for the adapted version of the
$q$-summing operators to the topology of the convergence of the vector
valued integrals on Banach function spaces. In the pursuit of this
objective we prove that the mere summability of the identity map does
not guaranty that the space has to be finite dimensional, contrarily to
the classical case. Some local compactness assumptions on the unit balls
are required. Our results open the door to new convergence theorems
and tools regarding summability of series of integrable functions and
approximation in function spaces, since we may find infinite dimensional
spaces in which convergence of the integrals ---our vector valued version
of convergence in the weak topology--- is equivalent to the convergence
with respect to the norm. Examples and applications are also given.
Archive classification: math.FA
Mathematics Subject Classification: 46B15, 46B50, 46E30, 46G10
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/1507.03033
or
http://arXiv.org/abs/1507.03033
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ben Wallis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 14:47:37 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Closed ideals in $\mathcal{L}(X)$
and $\mathcal{L}(X^*)$ when $X$ contains certain copies of $\ell_p$
and $c_0$" by Ben Wallis.
Abstract:
Suppose $X$ is a real or complexified Banach space containing a
complemented copy of $\ell_p$, $p\in(1,2)$, and a copy (not necessarily
complemented) of either $\ell_q$, $q\in(p,\infty)$, or $c_0$. Then
$\mathcal{L}(X)$ and $\mathcal{L}(X^*)$ each admit continuum many closed
ideals. If in addition $q\geq p'$, $\frac{1}{p}+\frac{1}{p'}=1$, then the
closed ideals of $\mathcal{L}(X)$ and $\mathcal{L}(X^*)$ each fail to be
linearly ordered. We obtain additional results in the special cases of
$\mathcal{L}(\ell_1\oplus\ell_q)$ and $\mathcal{L}(\ell_p\oplus c_0)$,
$1<p<2<q<\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 28 pages
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/1507.03241
or
http://arXiv.org/abs/1507.03241
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej Kurka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 14:48:58 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Zippin's embedding theorem and
amalgamations of classes of Banach" by Ondrej Kurka.
Abstract:
It was proved by Dodos and Ferenczi that the classes of Banach spaces
with a separable dual and of separable reflexive Banach spaces are
strongly bounded. In this note, we provide an isometric version of
this result.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B10, 46B15,
46B70 (Secondary)
Submitted from: kurka.ondrej at seznam.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.03899
or
http://arXiv.org/abs/1507.03899
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stefan Brach, Enrique A. Sanchez Perez and
Dirk Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Jul 2015 14:50:21 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Daugavet equation for bounded
vector valued functions" by Stefan Brach, Enrique A. Sanchez Perez and
Dirk Werner.
Abstract:
Requirements under which the Daugavet equation and the alternative
Daugavet equation hold for pairs of nonlinear maps between Banach spaces
are analysed. A geometric description is given in terms of nonlinear
slices. Some local versions of these properties are also introduced and
studied, as well as tests for checking if the required conditions are
satisfied in relevant cases.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B25, 46B80
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.04185
or
http://arXiv.org/abs/1507.04185
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Araujo, L. Bernal-Gonzalez, G.A.
Munoz-Fernandez, J.A. Prado-Bassas and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:18:16 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Lineability in sequence and
function spaces" by G. Araujo, L. Bernal-Gonzalez, G.A. Munoz-Fernandez,
J.A. Prado-Bassas and J.B. Seoane-Sepulveda.
Abstract:
It is proved the existence of large algebraic structures \break
--including large vector subspaces or infinitely generated free algebras--
inside, among others, the family of Lebesgue measurable functions that
are surjective in a strong sense, the family of nonconstant differentiable
real functions vanishing on dense sets, and the family of non-continuous
separately continuous real functions. Lineability in special spaces of
sequences is also investigated. Some of our findings complete or extend
a number of results by several authors.
Archive classification: math.FA
Mathematics Subject Classification: 28A20
Remarks: 18 pages, 1 figure
Submitted from: bassas at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.04477
or
http://arXiv.org/abs/1507.04477
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:19:45 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Separable determination of
(generalized-)lushness" by Marek Cuth.
Abstract:
We prove that every Asplund lush space is generalized-lush using
the method of separable reduction. This gives a partial positive answer
to a question by Jan-David Hardtke.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 46B20
Submitted from: cuth at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.05709
or
http://arXiv.org/abs/1507.05709
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by khalil saadi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:21:20 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the composition ideals of
Lipschitz mappings" by khalil saadi.
Abstract:
We study in this paper some property of Lipschitz mappings which admit
factorization through an operator ideal. We try to construct Lipschitz
cross-norms from known tensor norms in order to represent certain classes
of Lipschitz mappings. Inspired by the definition of p-summing linear
operators we introduce a new concpet in the the category of Lipschitz
mappings that is called strictly Lipschitz p-summing.
Archive classification: math.FA
Mathematics Subject Classification: [2000] 47B10, 46B28, 47L20
Report Number: 21 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/1507.05872
or
http://arXiv.org/abs/1507.05872
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernando Albiac, Jose L. Ansorena, Oscar
Ciaurri and Juan L. Varona
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:24:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Unconditional and quasi-greedy
bases in $L_p$ with applications to Jacobi polynomials Fourier series"
by Fernando Albiac, Jose L. Ansorena, Oscar Ciaurri and Juan L. Varona.
Abstract:
We show that the decreasing rearrangement of the Fourier series with
respect to the Jacobi polynomials for functions in $L_p$ does not
converge unless $p=2$. As a by-product of our work on quasi-greedy bases
in $L_{p}(\mu)$, we show that no normalized unconditional basis in $L_p$,
$p\not=2$, can be semi-normalized in $L_q$ for $q\not=p$, thus extending
a classical theorem of Kadets and Pe{\l}czy{\'n}ski from 1968.
Archive classification: math.FA
Mathematics Subject Classification: 46B15 (Primary) 41A65 (Secondary)
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/1507.05934
or
http://arXiv.org/abs/1507.05934
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Lechner and Markus Passenbrunner
and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:25:41 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Estimating averages of order
statistics of bivariate functions" by Richard Lechner and Markus
Passenbrunner and Joscha Prochno.
Abstract:
We prove uniform estimates for the expected value of averages of order
statistics of bivariate functions in terms of their largest values by a
direct analysis. As an application, uniform estimates for the expected
value of averages of order statistics of sequences of independent random
variables in terms of Orlicz norms are obtained. In the case where the
bivariate functions are matrices, we provide a ``minimal'' probability
space which allows us to $C$-embed certain Orlicz spaces $\ell_M^n$
into $\ell_1^{cn^3}$, $c,C>0$ being absolute constants.
Archive classification: math.PR math.FA math.ST stat.TH
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/1507.06227
or
http://arXiv.org/abs/1507.06227
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland, Ryan Causey, Daniel
Freeman, and Ben Wallis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 23 Jul 2015 15:27:11 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Class of operators determined
by ordinal indices" by Kevin Beanland, Ryan Causey, Daniel Freeman,
and Ben Wallis.
Abstract:
We introduce and study the Bourgain index of an operator between two
Banach spaces. In particular, we study the Bourgain $\ell_p$ and $c_0$
indices of an operator. Several estimates for finite and infinite direct
sums are established. We define classes determined by these indices and
show that some of these classes form operator ideals. We characterize the
ordinals which occur as the index of an operator and establish exactly
when the defined classes are closed. We study associated indices for
non-preservation of $\ell_p^\xi$ and $c_0^\xi$ spreading models and
indices characterizing weak compactness of operators between separable
Banach spaces. We also show that some of these classes are operator
ideals and discuss closedness and distinctness of these classes.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Remarks: 45 pages
Submitted from: kbeanland at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.06285
or
http://arXiv.org/abs/1507.06285
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Amiran Gogatishvili, Rza Mustafayev, and
Tugce Unver
From: alspach at pelczynski.math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 14:54:19 -0500 (CDT)
To: <banach at mathdept.okstate.edu>,<alspach at pelczynski.math.okstate.edu>
This is an announcement for the paper "Embeddings between weighted Copson
and Ces\`{a}ro function spaces" by Amiran Gogatishvili, Rza Mustafayev,
and Tugce Unver.
Abstract:
In this paper embeddings between weighted Copson function spaces
${\operatorname{Cop}}_{p_1,q_1}(u_1,v_1)$ and weighted Ces\`{a}ro
function spaces ${\operatorname{Ces}}_{p_2,q_2}(u_2,v_2)$ are
characterized. In particular, two-sided estimates of the optimal
constant $c$ in the inequality \begin{equation*} \bigg( \int_0^{\infty}
\bigg( \int_0^t f(\tau)^{p_2}v_2(\tau)\,d\tau\bigg)^{\frac{q_2}{p_2}}
u_2(t)\,dt\bigg)^{\frac{1}{q_2}} \le c \bigg( \int_0^{\infty} \bigg(
\int_t^{\infty} f(\tau)^{p_1} v_1(\tau)\,d\tau\bigg)^{\frac{q_1}{p_1}}
u_1(t)\,dt\bigg)^{\frac{1}{q_1}}, \end{equation*} where
$p_1,\,p_2,\,q_1,\,q_2 \in (0,\infty)$, $p_2 \le q_2$ and
$u_1,\,u_2,\,v_1,\,v_2$ are weights on $(0,\infty)$, are obtained. The
most innovative part consists of the fact that possibly different
parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$
and $v_2$ are allowed. The proof is based on the combination duality
techniques with estimates of optimal constants of the embeddings between
weighted Ces\`{a}ro and Copson spaces and weighted Lebesgue spaces,
which reduce the problem to the solutions of the iterated Hardy-type
inequalities.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46E30, Secondary 26D10
Remarks: 25 pages
Submitted from: rzamustafayev at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.07866
or
http://arXiv.org/abs/1507.07866
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Skillicorn
From: alspach at pelczynski.math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 14:55:38 -0500 (CDT)
To: <banach at mathdept.okstate.edu>,<alspach at pelczynski.math.okstate.edu>
This is an announcement for the paper "The uniqueness-of-norm problem
for Calkin algebras" by Richard Skillicorn.
Abstract:
We examine the question of whether the Calkin algebra of a Banach
space must have a unique complete algebra norm. We present a survey
of known results, and make the observation that a recent Banach space
construction of Argyros and Motakis (preprint, 2015) provides the first
negative answer. The parallel question for the weak Calkin algebra also
has a negative answer; we demonstrate this using a Banach space of 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/1507.08118
or
http://arXiv.org/abs/1507.08118
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Edmunds, Amiran Gogatishvili, Tengiz
Kopaliani and Nino Samashvili
From: alspach at pelczynski.math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:01:19 -0500 (CDT)
To: <banach at mathdept.okstate.edu>,<alspach at pelczynski.math.okstate.edu>
This is an announcement for the paper "Some $s$-numbers of an integral
operator of Hardy type in Banach function spaces" by David Edmunds,
Amiran Gogatishvili, Tengiz Kopaliani and Nino Samashvili.
Abstract:
Let $s_{n}(T)$ denote the $n$th approximation, isomorphism, Gelfand,
Kolmogorov or Bernstein number of the Hardy-type integral operator $T$
given by
$$
Tf(x)=v(x)\int_{a}^{x}u(t)f(t)dt,\,\,\,x\in(a,b)\,\,(-\infty<a<b<+\infty)
$$ and mapping a Banach function space $E$ to itself. We investigate
some geometrical properties of $E$ for which
$$ C_{1}\int_{a}^{b}u(x)v(x)dx
\leq\limsup\limits_{n\rightarrow\infty}ns_{n}(T)
\leq \limsup\limits_{n\rightarrow\infty}ns_{n}(T)\leq
C_{2}\int_{a}^{b}u(x)v(x)dx $$
under appropriate conditions on $u$
and $v.$ The constants $C_{1},C_{2}>0$ depend only on the space $E.$
Archive classification: math.FA math.AP math.CA
Mathematics Subject Classification: 35P30, 46E30, 46E35, 47A75 47B06,
47B10, 47B40, 47G10
Submitted from: gogatish at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.08854
or
http://arXiv.org/abs/1507.08854
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bernardo Cascales, Jose Orihuela and
Antonio Perez
From: alspach at pelczynski.math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:03:29 -0500 (CDT)
To: <banach at mathdept.okstate.edu>,<alspach at pelczynski.math.okstate.edu>
This is an announcement for the paper "One side James' Compactness
Theorem" by Bernardo Cascales, Jose Orihuela and Antonio Perez.
Abstract:
We present some extensions of classical results that involve elements of
the dual of Banach spaces, such as Bishop-Phelp's theorem and James'
compactness theorem, but restricting to sets of functionals determined
by geometrical properties. The main result, which answers a question
posed by F. Delbaen, is the following: Let $E$ be a Banach space such
that $(B_{E^\ast}, \omega^\ast)$ is convex block compact. Let $A$ and
$B$ be bounded, closed and convex sets with distance $d(A,B) > 0$. If
every $x^\ast \in E^\ast$ with \[ \sup(x^\ast,B) < \inf(x^\ast,A) \]
attains its infimum on $A$ and its supremum on $B$, then $A$ and $B$
are both weakly compact.
We obtain new characterizations of weakly compact sets and reflexive
spaces, as well as a result concerning a variational problem in dual
Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46A50, 46B50
Remarks: 18 pages
Submitted from: antonio.perez7 at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.00496
or
http://arXiv.org/abs/1508.00496
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey Astashkin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:19:36 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Rademacher functions in weighted
symmetric spaces" by Sergey Astashkin.
Abstract:
The closed span of Rademacher functions is investigated in the weighted
spaces X(w), where X is a symmetric space on [0,1] and w is a positive
measurable function on [0,1]. By using the notion and properties
of the Rademacher multiplicator space of a symmetric space, we give
a description of the weights w for which the Rademacher orthogonal
projection is bounded in X(w).
Archive classification: math.FA
Mathematics Subject Classification: 46E30 (Primary), 46B20, 46B42
(Secondary)
Remarks: 15 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/1508.00734
or
http://arXiv.org/abs/1508.00734
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by T. Figiel and W. B. Johnson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:36:36 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The Dual Form of the
Approximation Property for a Banach Space and a Subspace" by T. Figiel
and W. B. Johnson.
Abstract:
Given a Banach space X and a subspace Y, the pair (X,Y) is said to have
the approximation property (AP) provided there is a net of finite rank
bounded linear operators on X all of which leave the subspace Y invariant
such that the net converges uniformly on compact subsets of X to the
identity operator. The main result is an easy to apply dual formulation
of this property. Applications are given to three space properties;
in particular, if X has the approximation property and its subspace Y
is script L-infinity, then X/Y has the approximation property.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46B20, 46B28
Submitted from: johnson at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.01212
or
http://arXiv.org/abs/1508.01212
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ryan M Causey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:38:21 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An ordinal index characterizing
weak compactness of operators" by Ryan M Causey.
Abstract:
We introduce an ordinal index which characterizes weak compactness of
operators between Banach spaces. We study when classes consisting of
operators having bounded index form a closed ideal, the distinctness of
the classes, and the descriptive set theoretic properties of this index.
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/1508.02065
or
http://arXiv.org/abs/1508.02065
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bruno de Mendonca Braga
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:39:53 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the complexity of some classes
of Banach spaces and" by Bruno de Mendonca Braga.
Abstract:
These notes are dedicated to the study of the complexity of several
classes of separable Banach spaces. We compute the complexity of the
Banach-Saks property, the alternating Banach-Saks property, the complete
continuous property, and the LUST property. We also show that the weak
Banach-Saks property, the Schur property, the Dunford-Pettis property,
the analytic Radon-Nikodym property, the set of Banach spaces whose set of
unconditionally converging operators is complemented in its bounded oper-
ators, the set of Banach spaces whose set of weakly compact operators is
complemented in its bounded operators, and the set of Banach spaces whose
set of Banach-Saks opera- tors is complemented in its bounded operators,
are all non Borel in SB. At last, we give several applications of those
results to non-universality results.
Archive classification: math.FA
Submitted from: demendoncabraga at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.01960
or
http://arXiv.org/abs/1508.01960
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bruno de Mendonca Braga
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:41:09 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the complexity of some
inevitable classes of separable Banach" by Bruno de Mendonca Braga.
Abstract:
In this paper, we study the descriptive complexity of some inevitable
classes of Banach spaces. Precisely, as shown in [Go], every Banach
space either contains a hereditarily indecomposable subspace or an
unconditional basis, and, as shown in [FR], every Banach space either
contains a minimal subspace or a continuously tight subspace. In these
notes, we study the complexity of those inevitable classes as well as
the complexity of containing a subspace in any of those classes.
Archive classification: math.FA
Submitted from: demendoncabraga at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.01961
or
http://arXiv.org/abs/1508.01961
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan Rozendaal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:43:15 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Functional calculus for
$C_{0}$-groups using (co)type" by Jan Rozendaal.
Abstract:
We study the functional calculus properties of generators of
$C_{0}$-groups under type and cotype assumptions on the underlying Banach
space. In particular, we show the following.
Let $-\mathrm{i}A$ generate a $C_{0}$-group on a Banach space $X$
with type $p\in[1,2]$ and cotype $q\in[2,\infty)$. Then
$A$ has a bounded $\mathcal{H}^{\infty}$-calculus from
$\mathrm{D}_{A}(\tfrac{1}{p}-\tfrac{1}{q},1)$ to $X$, i.e.\
$f(A):\mathrm{D}_{A}(\tfrac{1}{p}-\tfrac{1}{q},1)\to X$ is bounded
for each bounded holomorphic function $f$ on a sufficiently
large strip. %Hence $A$ has a bounded calculus for the class of
bounded holomorphic functions which decay polynomially of order
$\alpha>\frac{1}{p}-\frac{1}{q}$ at infinity. Under additional geometric
assumptions, satisfied by $\mathrm{L}^{p}$-spaces, we cover the case
$\alpha=\frac{1}{p}-\frac{1}{q}$.
As a corollary of our main theorem, for sectorial operators we
quantify the gap between bounded imaginary powers and a bounded
$\mathcal{H}^{\infty}$-calculus in terms of the type and cotype of
the underlying Banach space. For cosine functions we obtain similar
results as for $C_{0}$-groups. We extend our results to $R$-bounded
operator-valued calculi, and we give an application to the theory of
rational approximation of $C_{0}$-groups.
Archive classification: math.FA math.NA
Mathematics Subject Classification: Primary 47A60, Secondary 47D03,
46B20, 42A45
Remarks: 25 pages
Submitted from: janrozendaalmath at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.02036
or
http://arXiv.org/abs/1508.02036
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bruno de Mendonca Braga
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Aug 2015 15:45:04 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Duality on Banach spaces and a
Borel parametrized version of Zippin's theorem" by Bruno de Mendonca
Braga.
Abstract:
Let SB be the standard coding for separable Banach spaces as subspaces
of $C(\Delta)$. In these notes, we show that if $\mathbb{B} \subset
\text{SB}$ is a Borel subset of spaces with separable dual, then
the assignment $X \mapsto X^*$ can be realized by a Borel function
$\mathbb{B}\to \text{SB}$. Moreover, this assignment can be done in
such a way that the functional evaluation is still well defined (Theorem
$1$). Also, we prove a Borel parametrized version of Zippin's theorem,
i.e., we prove that there exists $Z \in \text{SB}$ and a Borel function
that assigns for each $X \in \mathbb{B}$ an isomorphic copy of $X$
inside of $Z$ (Theorem $5$).
Archive classification: math.FA
Submitted from: demendoncabraga at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.02066
or
http://arXiv.org/abs/1508.02066
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Abasov,N., Megaled,A., and Pliev,M
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:02:18 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Dominated oprerators from
a lattice-normed space to a sequence Banach lattice" by Abasov,N.,
Megaled,A., and Pliev,M.
Abstract:
Abstract. We show that every dominated linear operator from an
Banach-Kantorovich space over atomless Dedekind complete vector lattice to
a sequence Banach lattice $l_p({\Gamma})$ or $c_0({\Gamma})$ is narrow. As
a conse- quence, we obtain that an atomless Banach lattice cannot have a
finite dimensional decomposition of a certain kind. Finally we show that
if a linear dominated operator T from lattice-normed space V to Banach-
Kantorovich space W is order narrow then the same is its exact dominant
$\ls T\rs$.
Archive classification: math.FA
Mathematics Subject Classification: 47H30, 46B42
Submitted from: martin.weber at tu-dresden.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.03275
or
http://arXiv.org/abs/1508.03275
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kobos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:03:34 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An uniform estimate of the relative
projection constant" by Tomasz Kobos.
Abstract:
The main goal of the paper is to provide a quantitative lower bound
greater than $1$ for the relative projection constant $\lambda(Y, X)$,
where $X$ is a subspace of $\ell_{2p}^m$ space and $Y \subset X$ is an
arbitrary hyperplane. As a consequence, we establish that for every
integer $n \geq 4$ there exists an $n$-dimensional normed space $X$
such that for an every hyperplane $Y$ and every projection $P:X \to
Y$ the inequality $||P|| > 1 + \left (2 \left ( n + 3 \right )^{2}
\right )^{-100(n+3)^2}$ holds. This gives a non-trivial lower bound in
a variation of problem proposed by Bosznay and Garay in $1986$.
Archive classification: math.FA
Mathematics Subject Classification: 47A58, 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/1508.03518
or
http://arXiv.org/abs/1508.03518
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D.T. Dzadzaeva and M.A. Pliev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:05:20 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Narrow operators on lattice-normed
spaces and vector measures" by D.T. Dzadzaeva and M.A. Pliev.
Abstract:
We consider linear narrow operators on lattice-normed spaces. We prove
that, under mild assumptions, every finite rank linear operator
is strictly narrow (before it was known that such operators are
narrow). Then we show that every dominated, order continuous linear
operator from a lattice-normed space over atomless vector lattice to an
atomic lattice-normed space is order narrow.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B99, Secondary 46G12
Submitted from: martin.weber at tu-dresden.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.03995
or
http://arXiv.org/abs/1508.03995
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Timur Oikhberg and Pedro Tradacete
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:09:29 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Almost disjointness preservers"
by Timur Oikhberg and Pedro Tradacete.
Abstract:
We study the stability of disjointness preservers on Banach lattices. In
many cases, we prove that an ``almost disjointness preserving'' operator
is well approximable by a disjointess preserving one. However, this
approximation is not always possible, as our examples show.
Archive classification: math.FA
Mathematics Subject Classification: 47B38, 46B42
Remarks: 43 pages
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/1508.04074
or
http://arXiv.org/abs/1508.04074
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej Kurka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:11:23 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Non-universal families of separable
Banach spaces" by Ondrej Kurka.
Abstract:
We prove that if $ C $ is a family of separable Banach spaces which is
analytic with respect to the Effros-Borel structure and none member
of $ C $ is isometrically universal for all separable Banach spaces,
then there exists a separable Banach space with a monotone Schauder
basis which is isometrically universal for $ C $ but still not for all
separable Banach spaces. We also establish an analogous result for the
class of strictly convex spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B15, 46B20,
46B25 (Secondary)
Submitted from: kurka.ondrej at seznam.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.05059
or
http://arXiv.org/abs/1508.05059
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Miguel Zapata
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:19:35 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On conditional weak topologies
under a simplified approach derived the framework of conditional sets"
by Jose Miguel Zapata.
Abstract:
The purpose of this manuscript is to introduce a simplified approach
derived from the framework of conditional sets, which is a novel
approach to study dynamic and conditional settings, as those that
arise in mathematical finance. Under this approach, and with the aim
of providing an analytic basis for the study of dynamic and conditional
risk measures, we carry out a study of the conditional weak topologies
and conditional weak compactness, extending some well-known results to
this framework and culminating with the proof of conditional versions of
Eberlein-\v{S}mulian and Amir-Lindenstrauss Theorems. In pursuing this
aim we study the algebraic structure of conditional spaces conditionally
finitely generated and state conditional versions of Baire Category
Theorem and Uniform Boundedness Principle.
Archive classification: math.FA
Submitted from: jmzg1 at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.05112
or
http://arXiv.org/abs/1508.05112
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andreas Defant and Mieczyslaw Mastylo
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:21:42 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Bohnenblust-Hille inequalities
for Lorentz spaces via interpolation" by Andreas Defant and Mieczyslaw
Mastylo.
Abstract:
We prove that the Lorentz sequence space $\ell_{\frac{2m}{m+1},1}$
is, in a~precise sense, optimal among all symmetric Banach sequence
spaces satisfying a Bohnenblust-Hille type inequality for $m$-linear
forms or $m$-homogeneous polynomials on $\mathbb{C}^n$. Motivated by this
result we develop methods for dealing with subtle Bohnenblust-Hille type
inequalities in the setting of Lorentz spaces. Based on an interpolation
approach and the Blei-Fournier inequalities involving mixed type spaces,
we prove multilinear and polynomial Bohnenblust-Hille type inequalities in
Lorentz spaces with subpolynomial and subexponential constants. Improving
a remarkable result of Balasubramanian-Calado-Queff\'{e}lec, we show an
application to the theory of Dirichlet series.
Archive classification: math.FA
Mathematics Subject Classification: 46B70, 47A53
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/1508.05554
or
http://arXiv.org/abs/1508.05554
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andreas Defant and Mieczyslaw Mastylo
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:23:28 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "$L^p$-norms and Mahler's measure
of polynomials on the $n$-dimensional torus" by Andreas Defant and
Mieczyslaw Mastylo.
Abstract:
We prove Nikol'skii type inequalities which for polynomials on the
$n$-dimensional torus $\mathbb{T}^n$ relate the $L^p$-with the $L^q$-norm
(with respect to the normalized Lebesgue measure and $0 <p <q <
\infty$). Among other things we show that $C=\sqrt{q/p}$ is the best
constant such that $\|P\|_{L^q}\leq C^{\text{deg}(P)} \|P\|_{L^p}$ for
all homogeneous polynomials $P$ on $\mathbb{T}^n$. We also prove an exact
inequality between the $L^p$-norm of a polynomial $P$ on $\mathbb{T}^n$
and its Mahler measure $M(P)$, which is the geometric mean of $|P|$
with respect to the normalized Lebesgue measure on $\mathbb{T}^n$. Using
extrapolation we transfer this estimate into a Khintchine-Kahane type
inequality, which, for polynomials on $\mathbb{T}^n$, relates a certain
exponential Orlicz norm and Mahler's measure. Applications are given,
including some interpolation estimates.
Archive classification: math.FA
Mathematics Subject Classification: 11R06, 11C08
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/1508.05556
or
http://arXiv.org/abs/1508.05556
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ramon van Handel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Aug 2015 14:25:10 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Chaining, Interpolation, and
Convexity" by Ramon van Handel.
Abstract:
We show that classical chaining bounds on the suprema of random
processes in terms of entropy numbers can be systematically improved
when the underlying set is convex: the entropy numbers need not be
computed for the entire set, but only for certain "thin" subsets. This
phenomenon arises from the observation that real interpolation can be used
as a natural chaining mechanism. Unlike the general form of Talagrand's
generic chaining method, which is sharp but often difficult to use, the
resulting bounds involve only entropy numbers but are nonetheless sharp
in many situations in which classical entropy bounds are suboptimal. Such
bounds are readily amenable to explicit computations in specific examples,
and we discover some old and new geometric principles for the control
of chaining functionals as special cases.
Archive classification: math.PR math.FA math.MG
Mathematics Subject Classification: 60B11, 60G15, 41A46, 46B20, 46B70
Remarks: 20 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/1508.05906
or
http://arXiv.org/abs/1508.05906
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal Analysis Seminar at Kent State, November 14-15.
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Wed, 2 Sep 2015 14:25:33 -0400 (13:25 CDT)
To: <banach at mathdept.okstate.edu>
Dear Colleague,
The Analysis group at Kent State University is happy to announce
a meeting of the Informal Analysis Seminar, which will be held at the
Department of Mathematical Sciences at Kent State University, November
14-15, 2015.
The plenary lecture series will be given by:
Boaz Klartag (Tel Aviv University)
and
Igor Rivin (University of St. Andrews)
Each speaker will deliver a four hour lecture series designed to be
accessible for graduate students.
Funding is available to cover the local and travel expenses of a limited
number of participants. Graduate students, postdoctoral researchers,
and members of underrepresented groups are particularly encouraged to
apply for support.
A poster session will be held for researchers to display their work.
Graduate students are particularly encouraged to submit a poster.
Posters can be submitted electronically in PDF format before November 6,
2015.
Further information, and an online registration form, can be found online
http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/November_2015.html
We encourage you to register as soon as possible, but to receive support
and/or help with hotel reservation, please, register before October 1,
2015.
Please feel free to contact us at informal at math.kent.edu for any
further information.
Sincerely,
Analysis Group at Kent State University
_______________________________________________
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 Victor Bible and Richard J. Smith
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:38:47 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Smooth and polyhedral approximation
in Banach spaces" by Victor Bible and Richard J. Smith.
Abstract:
We show that norms on certain Banach spaces $X$ can be approximated
uniformly, and with arbitrary precision, on bounded subsets of $X$ by
$C^{\infty}$ smooth norms and polyhedral norms. In particular, we show
that this holds for any equivalent norm on $c_0(\Gamma)$, where $\Gamma$
is an arbitrary set. We also give a necessary condition for the existence
of a polyhedral norm on a weakly compactly generated Banach space,
which extends a well-known result of Fonf.
Archive classification: math.FA
Mathematics Subject Classification: 46B03 46B20
Remarks: 12 pages
Submitted from: victor.bible at ucdconnect.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.00369
or
http://arXiv.org/abs/1509.00369
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephane Chretien and Sebastien Darses
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:39:58 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "An elementary approach to the
problem of column selection in a rectangular matrix" by Stephane Chretien
and Sebastien Darses.
Abstract:
The problem of extracting a well conditioned submatrix from any
rectangular matrix (with normalized columns) has been
studied for some time in functional and harmonic analysis; see
\cite{BourgainTzafriri:IJM87,Tropp:StudiaMath08,Vershynin:IJM01} for
methods using random column selection. More constructive approaches
have been proposed recently; see the recent contributions of
\cite{SpielmanSrivastava:IJM12,Youssef:IMRN14}. The column selection
problem we consider in this paper is concerned with extracting a well
conditioned submatrix, i.e. a matrix whose singular values all lie
in $[1-\epsilon,1+\epsilon]$. We provide individual lower and upper
bounds for each singular value of the extracted matrix at the price of
conceding only one log factor in the number of columns, when compared
to the Restricted Invertibility Theorem of Bourgain and Tzafriri. Our
method is fully constructive and the proof is short and elementary.
Archive classification: math.FA math.SP
Remarks: 5 pages
Submitted from: stephane.chretien at npl.co.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.00748
or
http://arXiv.org/abs/1509.00748
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Flores, Francisco L. Hernandez and
Pedro Tradacete
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:41:28 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Disjointly homogeneous Banach
lattices and applications" by Julio Flores, Francisco L. Hernandez and
Pedro Tradacete.
Abstract:
This is a survey on disjointly homogeneous Banach lattices and their
applicactions. Several structural properties of this class are
analyzed. In addition we show how these spaces provide a natural
framework for studying the compactness of powers of operators allowing
for a unified treatment of well-known results.
Archive classification: math.FA
Mathematics Subject Classification: 47B38, 46E30
Remarks: 20 pages, to appear in Proceedings Positivity VII Conference
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/1509.01499
or
http://arXiv.org/abs/1509.01499
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gleb Sirotkin and Ben Wallis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:43:02 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Sequence-singular operators"
by Gleb Sirotkin and Ben Wallis.
Abstract:
In this paper we study two types of collections of operators on a Banach
space on the subject of forming operator ideals. One of the types allows
us to construct an uncountable chain of closed ideals in each of the
operator algebras $\mathcal{L}(\ell_1\oplus\ell_q)$, $1<q<\infty$, and
$\mathcal{L}(\ell_1\oplus c_0)$. This finishes answering a longstanding
question of Pietsch.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46B25, 46B45, 47L10, 47L20
Remarks: 13 pages
Submitted from: z1019463 at students.niu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.01485
or
http://arXiv.org/abs/1509.01485
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: Tue, 15 Sep 2015 15:44:53 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Diametral diameter two properties"
by Julio Becerra Guerrero, Gines Lopez Perez and Abraham Rueda Zoca.
Abstract:
The aim of this note is to define a generalization of the diameter two
properties in terms of the abundance of diametral points. We shall also
analyze the stability of these properties under $\ell_p$ sums and the
problem of inheritance to subspaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 25 pages
Submitted from: arz0001 at correo.ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.02061
or
http://arXiv.org/abs/1509.02061
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Olivier Guedon, Alexander E. Litvak, Alain
Pajor, and Nicole Tomczak-Jaegermann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:46:45 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the interval of fluctuation of
the singular values of random" by Olivier Guedon, Alexander E. Litvak,
Alain Pajor, and Nicole Tomczak-Jaegermann.
Abstract:
Let $A$ be a matrix whose columns $X_1,\dots, X_N$ are independent
random vectors in $\mathbb{R}^n$. Assume that the tails of the
1-dimensional marginals decay as $\mathbb{P}(|\langle X_i, a\rangle|\geq
t)\leq t^{-p}$ uniformly in $a\in S^{n-1}$ and $i\leq N$. Then for $p>4$
we prove that with high probability $A/{\sqrt{n}}$ has the Restricted
Isometry Property (RIP) provided that Euclidean norms $|X_i|$ are
concentrated around $\sqrt{n}$. We also show that the covariance matrix
is well approximated by the empirical covariance matrix and establish
corresponding quantitative estimates on the rate of convergence in terms
of the ratio $n/N$. Moreover, we obtain sharp bounds for both problems
when the decay is of the type $ \exp({-t^{\alpha}})$ with $\alpha \in
(0,2]$, extending the known case $\alpha\in[1, 2]$.
Archive classification: math.PR cs.IT math.FA math.IT
Mathematics Subject Classification: 60B20, 46B06, 15B52, 46B09, 60D05
Remarks: To appear in J. Eur. Math. Soc
Submitted from: olivier.guedon at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.02322
or
http://arXiv.org/abs/1509.02322
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nick Lindemulder
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:48:42 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Banach space-valued extensions
of linear operators on $L^{\infty}$" by Nick Lindemulder.
Abstract:
Let $E$ and $G$ be two Banach function spaces, let $T \in
\mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach
dual pair. In this paper we give conditions for which there
exists a (necessarily unique) bounded linear operator $T_{Y} \in
\mathcal{L}(E(Y),G(Y))$ with the property that \[ {\langle x,T_{Y}e
\rangle} = T{\langle x,e \rangle} \quad\quad \forall e \in E(Y), x \in
X. \]
Our first main result states that, in case ${\langle X,Y \rangle} =
{\langle Y^{*}, Y \rangle}$ with $Y$ a reflexive Banach space, for the
existence of $T_{Y}$ it sufficient that $T$ is dominated by a positive
operator.
Our second main result concerns the case that $T$ is an adjoint operator
on $L^{\infty}(A)$: we suppose that $E = L^{\infty}(A)$
for a semi-finite measure space $(A,\mathscr{A},\mu)$, that
${\langle F, G \rangle}$ is a K\"othe dual pair, and that $T$ is
$\sigma(L^{\infty}(A),L^{1}(A))$-to-$\sigma(G,F)$ continuous. Then $T_{Y}$
exists provided that $T$ is dominated by a positive operator, in which
case $T_{Y}$ is $\sigma(L^{\infty}(A;Y),L^{1}(A;X))$-to-$\sigma(G(Y),F
\tilde{\otimes} X)$ continuous; here $F \tilde{\otimes} X$ denotes
the closure of $F \otimes X$ in $F(X)$. We also consider situations in
which the existence is automatic and we furthermore show that in certain
situations it is necessary that $T$ is regular. As an application of
this result we consider conditional expectation on Banach space-valued
$L^{\infty}$-spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E40 (primary), 46E30, 46B10
(secondary)
Remarks: 20 pages
Submitted from: n.lindemulder at tudelft.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.02493
or
http://arXiv.org/abs/1509.02493
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Niels Jakob Laustsen, Richard Lechner, and
Paul F.X. Mueller
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 15 Sep 2015 15:50:13 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Factorization of the identity
through operators with large diagonal" by Niels Jakob Laustsen, Richard
Lechner, and Paul F.X. Mueller.
Abstract:
Given a Banach space $X$ with an unconditional basis, we consider the
following question: does the identity on $X$ factor through every
bounded operator on $X$ with large diagonal relative to the unconditional
basis? We show that on Gowers' space with its unconditional basis there
exists an operator for which the answer to the question is negative. By
contrast, for any operator on the mixed-norm Hardy spaces $H^p(H^q)$,
where $1 \leq p,q < \infty$, with the bi-parameter Haar system, this
problem always has a positive solution. The one-parameter $H^p$ spaces
were treated first by Andrew in 1979.
Archive classification: math.FA
Mathematics Subject Classification: 46B25, 60G46, 46B07, 46B26, 30H35,
30H10, 46B15, 47B37, 47A53
Remarks: 16 pages, 5 figures
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/1509.03141
or
http://arXiv.org/abs/1509.03141
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Transfinite methods in Banach spaces and algebras of
operators
From: Dale Alspach <alspach at math.okstate.edu>
Date: Sun, 20 Sep 2015 11:08:14 -0500
To: <banach at mathdept.okstate.edu>
Dear Colleague,
We are pleased to announce that a conference entitled "Transfinite
methods in Banach spaces and algebras of operators" will take place at
Bedlewo Conference Center, Poland, 18-22 July 2016.
The list of speakers will include:
Tristan Bice (Salvador), Christina Brech (Sao Paulo), Yemon Choi
(Lancaster; tbc), Marek Cuth (Prague), Garth Dales (Lancaster), Alan Dow
(North Carolina), Valentin Ferenczi (Sao Paulo), Joanna Garbulinska
(Kielce), Gilles Godefroy (Paris VI), Bill Johnson (Texas A&M; tbc),
Tomasz Kochanek (IM PAN), Jordi Lopez-Abad (ICMAT Madrid), Pavlos
Motakis (Texas A&M), Grzegorz Plebanek (Wroclaw), Jose Rodriguez
(Murcia), Thomas Schlumprecht (Texas A&M), Jesus Suarez (Caceres) and
Stevo Todorcevic (CRNS, Toronto).
For more details, please see the webpage:
http://www.impan.pl/~set_theory/Banach2016/
<http://www.impan.pl/%7Eset_theory/Banach2016/>
We would be very grateful if you could distribute this email to anybody
who might be interested in the conference, including graduate students
and early-career researchers.
We hope to see you in Bedlewo next summer!
Best wishes,
Antonio Aviles, Piotr Koszmider, Niels Laustsen
(we apologize if you received this e-mail more than once, or if you are
not interested)
_______________________________________________
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 Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:04:50 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the problem of compact totally
disconnected reflection of nonmetrizability" by Piotr Koszmider.
Abstract:
We construct a ZFC example of a nonmetrizable compact space $K$
such that every totally disconnected closed subspace $L\subseteq K$
is metrizable. In fact, the construction can be arranged so that every
nonmetrizable compact subspace may be of fixed big dimension. Then we
focus on the problem if a nonmetrizable compact space $K$ must have a
closed subspace with a nonmetrizable totally disconnected continuous
image. This question has several links with the the structure of the
Banach space $C(K)$, for example, by Holszty\'nski's theorem, if $K$ is a
counterexample, then $C(K)$ contains no isometric copy of a nonseparable
Banach space $C(L)$ for $L$ totally disconnected. We show that in the
literature there are diverse consistent counterexamples, most eliminated
by Martin's axiom and the negation of the continuum hypothesis, but some
consistent with it. We analyze the above problem for a particular class of
spaces. OCA+MA however, implies the nonexistence of any counterexample in
this class but the existence of some other absolute example remains open.
Archive classification: math.GN math.FA math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.05282
or
http://arXiv.org/abs/1509.05282
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tatiana Shulman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:06:38 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On subspaces of invariant vectors"
by Tatiana Shulman.
Abstract:
Let $X_{\pi}$ be the subspace of fixed vectors for a uniformly bounded
representation $\pi$ of a group $G$ on a Banach space $X$. We study the
problem of the existence and uniqueness of a subspace $Y$ that complements
$X_{\pi}$ in $X$. Similar questions for $G$-invariant complement to
$X_{\pi}$ are considered. We prove that every non-amenable discrete group
$G$ has a representation with non-complemented $X_{\pi}$ and find some
conditions that provide an $G$-invariant complement. A special attention
is given to representations on $C(K)$ that arise from an action of $G$
on a metric compact $K$.
Archive classification: math.FA
Mathematics Subject Classification: 22A25, 46B99, 22D25
Submitted from: tatiana_shulman at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.05263
or
http://arXiv.org/abs/1509.05263
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gonzalo Martinez-Cervantes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:08:26 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On weakly Radon-Nikod\'ym compact
spaces" by Gonzalo Martinez-Cervantes.
Abstract:
A compact space is said to be weakly Radon-Nikod\'ym if it is
homeomorphic to a weak*-compact subset of the dual of a Banach space not
containing an isomorphic copy of $\ell_1$. In this work we provide an
example of a continuous image of a Radon-Nikod\'ym compact space which
is not weakly Radon-Nikod\'ym. Moreover, we define a superclass of the
continuous images of weakly Radon-Nikod\'ym compact spaces and study
its relation with Corson compacta and weakly Radon-Nikod\'ym compacta.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46B22, 46B50, 54G20
Submitted from: gonzalo.martinez2 at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.05324
or
http://arXiv.org/abs/1509.05324
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Silouanos Brazitikos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:10:13 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Brascamp-Lieb inequality and
quantitative versions of Helly's theorem" by Silouanos Brazitikos.
Abstract:
We provide a number of new quantitative versions of Helly's theorem. For
example, we show that for every family $\{P_i:i\in I\}$ of closed
half-spaces $$P_i=\{ x\in {\mathbb R}^n:\langle x,w_i\rangle \leq 1\}$$
in ${\mathbb R}^n$ such that $P=\bigcap_{i\in I}P_i$ has positive volume,
there exist $s\leq \alpha n$ and $i_1,\ldots , i_s\in I$ such that
$$|P_{i_1}\cap\cdots\cap P_{i_s}|\leq (Cn)^n\,|P|,$$ where $\alpha , C>0$
are absolute constants. These results complement and improve previous
work of B\'{a}r\'{a}ny-Katchalski-Pach and Nasz\'{o}di. Our method
combines the work of Srivastava on approximate John's decompositions
with few vectors, a new estimate on the corresponding constant in the
Brascamp-Lieb inequality and an appropriate variant of Ball's proof of
the reverse isoperimetric inequality.
Archive classification: math.FA
Mathematics Subject Classification: 26D15
Submitted from: silouanb at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.05783
or
http://arXiv.org/abs/1509.05783
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Zhe-Ming Zheng and Hui-Sheng Ding
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:11:57 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "A note on closedness of the
sum of two closed subspaces in a Banach space" by Zhe-Ming Zheng and
Hui-Sheng Ding.
Abstract:
Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We
present several necessary and sufficient conditions for the closedness
of $M+N$ ($M+N$ is not necessarily direct sum).
Archive classification: math.FA
Submitted from: dinghs at mail.ustc.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.06445
or
http://arXiv.org/abs/1509.06445
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hana Krulisova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:13:50 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Quantification of Pe\l czy\'nski's
property (V)" by Hana Krulisova.
Abstract:
A Banach space $X$ has Pe\l czy\' nski's property (V) if for every
Banach space $Y$ every unconditionally converging operator $T\colon
X\to Y$ is weakly compact. In 1962, Aleksander Pe\l czy\' nski showed
that $C(K)$ spaces for a compact Hausdorff space $K$ enjoy the property
(V), and some generalizations of this theorem have been proved since
then. We introduce several possibilities of quantifying the property
(V). We prove some characterizations of the introduced quantitative
versions of this property, which allow us to prove a quantitative version
of Pelczynski's result about $C(K)$ spaces and generalize it. Finally, we
study the relationship of several properties of operators including weak
compactness and unconditional convergence, and using the results obtained
we establish a relation between quantitative versions of the property (V)
and quantitative versions of other well known properties of Banach spaces.
Archive classification: math.FA
Remarks: 19 pages
Submitted from: krulisova at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.06610
or
http://arXiv.org/abs/1509.06610
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigory Ivanov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:15:30 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Hypomonotonicity of the normal
cone and proximal smoothness" by Grigory Ivanov.
Abstract:
In this paper we study the properties of the normal cone to the
proximally smooth set. We give the complete characterization of the
proximally smooth set through the monotony properties of its normal cone
in an arbitrary uniformly convex and uniformly smooth Banach space. We
give the exact bounds for right-hand side in the monotonicity inequality
for normal cone in terms of the moduli of smoothness and convexity of
a Banach space.
Archive classification: math.FA
Submitted from: grigory.ivanov at phystech.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.06795
or
http://arXiv.org/abs/1509.06795
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gleb Sirotkin and Ben Wallis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:16:52 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Almost-invariant and
essentially-invariant halfspaces" by Gleb Sirotkin and Ben Wallis.
Abstract:
In this paper we study sufficient conditions for an operator to have an
almost-invariant half-space. As a consequence, we show that if $X$
is an infinite-dimensional complex Banach space then every operator
$T\in\mathcal{L}(X)$ admits an essentially-invariant half-space. We also
show that whenever a closed algebra of operators possesses a common AIHS,
then it has a common invariant half-space as well.
Archive classification: math.FA
Mathematics Subject Classification: 15A03, 15A18, 15A60, 47L10, 47A10,
47A11, 47A15
Remarks: 11 pages. Keywords: functional analysis, Banach spaces,
surjectivity
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.07428
or
http://arXiv.org/abs/1509.07428
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Niushan Gao, Vladimir G. Troitsky, and
Foivos Xanthos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:18:48 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Uo-convergence and its
applications to Ces\`aro means in Banach lattices" by Niushan Gao,
Vladimir G. Troitsky, and Foivos Xanthos.
Abstract:
A net $(x_\alpha)$ in a vector lattice $X$ is said to uo-converge to
$x$ if $|x_\alpha-x|\wedge u\xrightarrow{\rm o}0$ for every $u\ge 0$. In
the first part of this paper, we study some functional-analytic aspects
of uo-convergence. We prove that uo-convergence is stable under passing
to and from regular sublattices. This fact leads to numerous applications
presented throughout the paper. In particular, it allows us to improve
several results in [26,27]. In the second part, we use uo-convergence to
study convergence of Ces\`aro means in Banach lattices. In particular,
we establish an intrinsic version of Koml\'os' Theorem, which extends
the main results of [35,16,31] in a uniform way. We also develop a new
and unified approach to Banach-Saks properties and Banach-Saks operators
based on uo-convergence. This approach yields, in particular, short
direct proofs of several results in [21,24,25].
Archive classification: math.FA
Remarks: 45 pages
Submitted from: foivos at ryerson.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.07914
or
http://arXiv.org/abs/1509.07914
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:21:12 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On certain Opial-type results in
Ces\`aro spaces of vector-valued functions" by Jan-David Hardtke.
Abstract:
Given a Banach space $X$, we consider Ces\`aro spaces $\text{Ces}_p(X)$
of $X$-valued functions over the interval $[0,1]$, where $1\leq
p<\infty$. We prove that if $X$ has the Opial/uniform Opial property,
then certain analogous properties also hold for $\text{Ces}_p(X)$. We
also prove a result on the Opial/uniform Opial property of Ces\`aro
spaces of vector-valued sequences.
Archive classification: math.FA
Mathematics Subject Classification: 46E40 46E30 46B20
Remarks: 15 pages, partial text overlap with arXiv:1403.2647
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/1509.08097
or
http://arXiv.org/abs/1509.08097
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Santeri Miihkinen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 29 Sep 2015 14:22:35 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Strict singularity of a
Volterra-type integral operator on $H^p$" by Santeri Miihkinen.
Abstract:
We prove that a Volterra-type integral operator $T_gf(z) = \int_0^z
f(\zeta)g'(\zeta)d\zeta, \, z \in \mathbb D,$ defined on Hardy spaces
$H^p, \, 1 \le p < \infty,$ fixes an isomorphic copy of $\ell^p,$ if the
operator $T_g$ is not compact. In particular, this shows that the strict
singularity of the operator $T_g$ coincides with the compactness of the
operator $T_g$ on spaces $H^p.$ As a consequence, we obtain a new proof
for the equivalence of the compactness and the weak compactness of the
operator $T_g$ on $H^1$.
Archive classification: math.FA
Mathematics Subject Classification: 47G10 (Primary) 30H10 (Secondary )
Remarks: 14 pages, 1 figure
Submitted from: santeri.miihkinen at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.08356
or
http://arXiv.org/abs/1509.08356
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Analytic and Probabilistic Techniques in Modern Convex
Geometry, Nov 7-9, 2015
From: "Pivovarov, Peter" <pivovarovp at missouri.edu>
Date: Thu, 1 Oct 2015 03:50:42 +0000
To: "banach at mathdept.okstate.edu" <banach at mathdept.okstate.edu>
Dear Colleagues:
The Mathematics Department at the University of Missouri-Columbia is
pleased to host a conference on Analytic and Probabilistic Techniques
in Modern Convex Geometry, dedicated to Alexander Koldobsky on the
occassion of his 60th birthday, November 7-9, 2015.
We aim to bring together experienced and early-stage researchers to
discuss the latest developments on slicing inequalities for convex
sets, geometry of high-dimensional measures, affine isoperimetric
inequalities and non-asymptotic random matrix theory.
Information is available at
http://www.bengal.missouri.edu/~pivovarovp/APTMCG/index.html
Funding is still available to cover the local and travel expenses of a
limited number of participants. Graduate students, postdoctoral
researchers, and members of underrepresented groups are particularly
encouraged to apply for support. Please register online or contact
Peter Pivovarov at pivovarovp at missouri.edu.
A poster session will be held for researchers to display their work.
Graduate students are particularly encouraged to submit a poster.
Yours sincerely,
Peter Pivovarov
on behalf of the organizers:
Grigoris Paouris
Peter Pivovarov
Mark Rudelson
Artem Zvavitch
_______________________________________________
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 Alexandr Andoni, Assaf Naor, and Ofer
Neiman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:04:03 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Snowflake universality of
Wasserstein spaces" by Alexandr Andoni, Assaf Naor, and Ofer Neiman.
Abstract:
For $p\in (1,\infty)$ let $\mathscr{P}_p(\mathbb{R}^3)$ denote the
metric space of all $p$-integrable Borel probability measures
on $\mathbb{R}^3$, equipped with the Wasserstein $p$ metric
$\mathsf{W}_p$. We prove that for every $\varepsilon>0$, every $\theta\in
(0,1/p]$ and every finite metric space $(X,d_X)$, the metric space
$(X,d_{X}^{\theta})$ embeds into $\mathscr{P}_p(\mathbb{R}^3)$ with
distortion at most $1+\varepsilon$. We show that this is sharp when
$p\in (1,2]$ in the sense that the exponent $1/p$ cannot be replaced
by any larger number. In fact, for arbitrarily large $n\in \mathbb{N}$
there exists an $n$-point metric space $(X_n,d_n)$ such that for every
$\alpha\in (1/p,1]$ any embedding of the metric space $(X_n,d_n^\alpha)$
into $\mathscr{P}_p(\mathbb{R}^3)$ incurs distortion that is at least a
constant multiple of $(\log n)^{\alpha-1/p}$. These statements establish
that there exists an Alexandrov space of nonnegative curvature,
namely $\mathscr{P}_{\! 2}(\mathbb{R}^3)$, with respect to which
there does not exist a sequence of bounded degree expander graphs. It
also follows that $\mathscr{P}_{\! 2}(\mathbb{R}^3)$ does not admit a
uniform, coarse, or quasisymmetric embedding into any Banach space of
nontrivial type. Links to several longstanding open questions in metric
geometry are discussed, including the characterization of subsets of
Alexandrov spaces, existence of expanders, the universality problem
for $\mathscr{P}_{\! 2}(\mathbb{R}^k)$, and the metric cotype dichotomy
problem.
Archive classification: math.MG math.FA
Submitted from: naor at math.princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.08677
or
http://arXiv.org/abs/1509.08677
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Xiao Chun Fang and Marat Pliev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:05:45 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Narrow Orthogonally Additive
Operators on Lattice-Normed Spaces" by Xiao Chun Fang and Marat Pliev.
Abstract:
The aim of this article is to extend results of M.~Popov and second
named author about orthogonally additive narrow operators on vector
lattices. The main object of our investigations are an orthogonally
additive narrow operators between lattice-normed spaces. We prove that
every $C$-compact laterally-to-norm continuous orthogonally additive
operator from a Banach-Kantorovich space $V$ to a Banach lattice $Y$
is narrow. We also show that every dominated Uryson operator from
Banach-Kantorovich space over an atomless Dedekind complete vector lattice
$E$ to a sequence Banach lattice $\ell_p(\Gamma)$ or $c_0(\Gamma)$ is
narrow. Finally, we prove that if an orthogonally additive dominated
operator $T$ from lattice-normed space $(V,E)$ to Banach-Kantorovich
space $(W,F)$ is order narrow then the order narrow is its exact dominant
$\ls T\rs$.
Archive classification: math.FA
Mathematics Subject Classification: 46B99. 47B99
Remarks: 16 pages
Submitted from: martin.weber at tu-dresden.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1509.09189
or
http://arXiv.org/abs/1509.09189
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas Hytonen, Sean Li, and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:07:16 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Quantitative affine approximation
for UMD targets" by Tuomas Hytonen, Sean Li, and Assaf Naor.
Abstract:
It is shown here that if $(Y,\|\cdot\|_Y)$ is a Banach space in which
martingale differences are unconditional (a UMD Banach space) then there
exists $c=c(Y)\in (0,\infty)$ with the following property. For every
$n\in \mathbb{N}$ and $\varepsilon\in (0,1/2]$, if $(X,\|\cdot\|_X)$
is an $n$-dimensional normed space with unit ball $B_X$ and $f:B_X\to
Y$ is a $1$-Lipschitz function then there exists an affine mapping
$\Lambda:X\to Y$ and a sub-ball $B^*=y+\rho B_X\subseteq B_X$ of radius
$\rho\ge \exp(-(1/\varepsilon)^{cn})$ such that $\|f(x)-\Lambda(x)\|_Y\le
\varepsilon \rho$ for all $x\in B^*$. This estimate on the macroscopic
scale of affine approximability of vector-valued Lipschitz functions is
an asymptotic improvement (as $n\to \infty$) over the best previously
known bound even when $X$ is $\mathbb{R}^n$ equipped with the Euclidean
norm and $Y$ is a Hilbert space.
Archive classification: math.FA math.MG
Submitted from: naor at math.princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.00276
or
http://arXiv.org/abs/1510.00276
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guillaume Aubrun and Stanislaw Szarek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:08:58 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Dvoretzky's theorem and the
complexity of entanglement detection" by Guillaume Aubrun and Stanislaw
Szarek.
Abstract:
The well-known Horodecki criterion asserts that a state $\rho$ on
$\mathbb{C}^d \otimes \mathbb{C}^d$ is entangled if and only if there
exists a positive map $\Phi : \mathsf{M}_d \to \mathsf{M}_d$ such
that the operator $(\Phi \otimes \mathsf{I})(\rho)$ is not positive
semi-definite. We show that that the number of such maps needed to
detect all the robustly entangled states (i.e., states $\rho$ which
remain entangled even in the presence of substantial randomizing noise)
exceeds $\exp(c d^3 / \log d)$. The proof is based on a study of the
approximability of the set of states (resp. of separable states) by
polytopes with few vertices or with few faces, and ultimately relies on
the Dvoretzky--Milman theorem about the dimension of almost spherical
sections of convex bodies. The result can be interpreted as a geometrical
manifestation of the complexity of entanglement detection.
Archive classification: quant-ph math.FA
Mathematics Subject Classification: 81P40, 46B07
Submitted from: aubrun at math.univ-lyon1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.00578
or
http://arXiv.org/abs/1510.00578
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joel Blot and Philippe Cieutat
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:11:05 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Completeness of Sums of Subspace
of Bounded Functions and Applications" by Joel Blot and Philippe Cieutat.
Abstract:
We give a new proof of a characterization of the closeness of the range
of a continuous linear operator and of the closeness of the sum of two
closed vector subspaces of a Banach space. Then we state sufficient
conditions for the closeness of the sum of two closed subspaces of the
Banach space of bounded functions and apply this result on various pseudo
almost periodic spaces and pseudo almost automorphic spaces.
Archive classification: math.FA
Submitted from: blot at univ-paris1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.01160
or
http://arXiv.org/abs/1510.01160
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Francisco J. Garcia-Pacheco, Alejandro
Miralles, and Daniele Puglisi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:13:16 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Dual maps and the Dunford-Pettis
property" by Francisco J. Garcia-Pacheco, Alejandro Miralles, and
Daniele Puglisi.
Abstract:
We characterize the points of $\left\|\cdot\right\|$-$w^*$ continuity of
dual maps, turning out to be the smooth points. We prove that a Banach
space has the Schur property if and only if it has the Dunford-Pettis
property and there exists a dual map that is sequentially $w$-$w$
continuous at $0$. As consequence, we show the existence of smooth Banach
spaces on which the dual map is not $w$-$w$ continuous at $0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B10
Remarks: 6 pages
Submitted from: mirallea at uji.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.01531
or
http://arXiv.org/abs/1510.01531
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Martin Dolezal, Martin Rmoutil, Benjamin
Vejnar, and Vaclav Vlasak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:15:39 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Haar meager sets revisited"
by Martin Dolezal, Martin Rmoutil, Benjamin Vejnar, and Vaclav Vlasak.
Abstract:
In the present article we investigate Darji's notion of Haar meager sets
from several directions. We consider alternative definitions and show
that some of them are equivalent to the original one, while others
fail to produce interesting notions. We define Haar meager sets in
nonabelian Polish groups and show that many results, including the
facts that Haar meager sets are meager and form a $\sigma$-ideal,
are valid in the more general setting as well. The article provides
various examples distinguishing Haar meager sets from Haar null sets,
including decomposition theorems for some subclasses of Polish groups. As
a corollary we obtain, for example, that $\mathbb Z^\omega$, $\mathbb
R^\omega$ or any Banach space can be decomposed into a Haar meager set and
a Haar null set. We also establish the stability of non-Haar meagerness
under Cartesian product.
Archive classification: math.GN math.FA
Remarks: 19 pages
Submitted from: dolezal at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.01613
or
http://arXiv.org/abs/1510.01613
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D.I. Florentin, V. D. Milman, and A. Segal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:17:13 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Identifying Set Inclusion by
Projective Positions and Mixed Volumes" by D.I. Florentin, V. D. Milman,
and A. Segal.
Abstract:
We study a few approaches to identify inclusion (up to a shift) between
two convex bodies in ${\mathbb R}^n$. To this goal we use mixed volumes
and fractional linear maps. We prove that inclusion may be identified
by comparing volume or surface area of all projective positions of the
sets. We prove similar results for Minkowski sums of the sets.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A05, 52A20, 52A38, 52A39, 51N15,
46B20
Citation: Identifying Set Inclusion by Projective Positions and Mixed
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.03844
or
http://arXiv.org/abs/1510.03844
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Martino Lupini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:20:25 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Fraisse limits in functional
analysis" by Martino Lupini.
Abstract:
We provide a unified approach to many Fra\"{\i}ss\'{e} limits in
functional analysis, including the Gurarij space, the Poulsen simplex, and
their noncommutative analogs. We recover in this general framework many
classical results about the Gurarij space and the Poulsen simplex, and at
the same time obtain their noncommutative generalizations. Particularly,
we construct noncommutative analogs of universal operators in the sense
of Rota.
Archive classification: math.FA math.LO math.OA
Mathematics Subject Classification: 46L07, 46A55 (Primary) 46L89, 03C30,
03C98 (Secondary)
Remarks: 28 pages
Submitted from: lupini at caltech.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.05188
or
http://arXiv.org/abs/1510.05188
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sofiya Ostrovska and Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 22 Oct 2015 13:21:52 -0500 (CDT)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Distortion in the finite
determination result for embeddings of finite metric spaces into Banach
spaces" by Sofiya Ostrovska and Mikhail I. Ostrovskii.
Abstract:
Given a Banach space $X$ and a locally finite metric space $A$, it is
known that if all finite subsets of $A$ admit bilipschitz embeddings
into $X$ with distortions $\le C$, then the space $A$ itself admits
an embedding into $X$ with distortion $\le D\cdot C$, where $D$ is
an absolute constant. The goal of this paper is to show that $D>1$,
implying that, in general, there is a ``deterioration of distortion''
in the aforementioned situations.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B85, 46B20
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.05974
or
http://arXiv.org/abs/1510.05974
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigoris Paouris, Petros Valettas and Joel
Zinn
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:19:39 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Random version of Dvoretzky's
theorem in $\ell_p^n$" by Grigoris Paouris, Petros Valettas and Joel Zinn.
Abstract:
We study the dependence on $\varepsilon$ in the critical dimension
$k(n, p, \varepsilon)$ that one can find random sections of the
$\ell_p^n$-ball which are $(1+\varepsilon)$-spherical. For any fixed $n$
we give lower estimates for $k(n, p, \varepsilon)$ for all eligible
values $p$ and $\varepsilon$, which agree with the sharp estimates
for the extreme values $p = 1$ and $p = \infty$. In order to do so,
we provide bounds for the gaussian concentration of the $\ell_p$-norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46B07, 46B09
Remarks: 45 pages
Submitted from: valettasp at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07284
or
http://arXiv.org/abs/1510.07284
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: Thu, 12 Nov 2015 12:23:22 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On Dvoretzky's theorem for
subspaces of $L_p$" by Grigoris Paouris and Petros Valettas.
Abstract:
We prove that for any $p > 2$ and every $n$-dimensional subspace $X$ of
$L_p$, the Euclidean space $\ell_2^k$ can be $(1 + \varepsilon)$-embedded
into $X$ with $k \geq c_p \min\{\varepsilon^2 n, (\varepsilon n)^{2/p}
\}$, where $c_p > 0$ is a constant depending only on $p$.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B07, 46B09
Remarks: 20 pages
Submitted from: valettasp at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07289
or
http://arXiv.org/abs/1510.07289
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miek Messerschmidt and Marten Wortel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:24:41 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The intrinsic metric on the unit
sphere of a normed space" by Miek Messerschmidt and Marten Wortel.
Abstract:
Let $S$ denote the unit sphere of a real normed space. We show that the
intrinsic metric on $S$ is strongly equivalent to the induced
metric on $S$. Specifically, for all $x,y\in S$, \[ \|x-y\|\leq
d(x,y)\leq\sqrt{2}\pi\|x-y\|, \] where $d$ denotes the intrinsic metric
on $S$.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary:46B10. Secondary: 51F99, 46B07
Submitted from: mmesserschmidt at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07442
or
http://arXiv.org/abs/1510.07442
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by L. Garcia-Lirola, J. Orihuela, and M. Raja
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:26:30 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Compact convex sets that admit
a lower semicontinuous strictly convex function" by L. Garcia-Lirola,
J. Orihuela, and M. Raja.
Abstract:
We study the class of compact convex subsets of a topological vector
space which admits a strictly convex and lower semicontinuous function. We
prove that such a compact set is embeddable in a strictly convex dual
Banach space endowed with its weak$^*$ topology. In addition, we find
exposed points where a strictly convex lower semicontinuous function
is continuous.
Archive classification: math.FA
Mathematics Subject Classification: 46A55 (Primary) 46B03, 54E35
(Secondary)
Remarks: 9 pages
Submitted from: luiscarlos.garcia at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.07921
or
http://arXiv.org/abs/1510.07921
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gonzalo Martinez-Cervantes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:28:12 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Riemann integrability versus weak
continuity" by Gonzalo Martinez-Cervantes.
Abstract:
In this paper we focus on the relation between Riemann integrability and
weak continuity. A Banach space $X$ is said to have the weak Lebesgue
property if every Riemann integrable function from $[0,1]$ into $X$
is weakly continuous almost everywhere. We prove that the weak Lebesgue
property is stable under $\ell_1$-sums and obtain new examples of Banach
spaces with and without this property. Furthermore, we characterize
Dunford-Pettis operators in terms of Riemann integrability and provide
a quantitative result about the size of the set of $\tau$-continuous
non Riemann integrable functions, with $\tau$ a locally convex topology
weaker than the norm topology.
Archive classification: math.FA
Mathematics Subject Classification: 46G10, 28B05, 03E10
Submitted from: gonzalo.martinez2 at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.08801
or
http://arXiv.org/abs/1510.08801
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Bernardo Gonzalez
Merino, Carlos Hugo Jimenez, and Rafael Villa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:30:00 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "John's ellipsoid and the integral
ratio of a log-concave function" by David Alonso-Gutierrez, Bernardo
Gonzalez Merino, Carlos Hugo Jimenez, and Rafael Villa.
Abstract:
We extend the notion of John's ellipsoid to the setting of integrable
log-concave functions. This will allow us to define the integral ratio
of a log-concave function, which will extend the notion of volume ratio,
and we will find the log-concave function maximizing the integral ratio. A
reverse functional a?ne isoperimetric inequality will be given, written in
terms of this integral ratio. This can be viewed as a stability version
of the functional affine isoperimetric inequality.
Archive classification: math.FA
Submitted from: bg.merino at tum.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.01266
or
http://arXiv.org/abs/1511.01266
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Kent E. Morrison
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:31:46 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The trace as an average over the
unit sphere of a normed space with a 1-symmetric basis" by Tomasz Kania
and Kent E. Morrison.
Abstract:
We generalise the formula expressing the matrix trace of a given square
matrix as the integral of the numerical values of $A$ over the Euclidean
sphere to the unit spheres of finite-dimensional normed spaces that have
a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms
in $\mathbb{R}^N$ for $p\neq 2$.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 15A60, 47A12
Submitted from: kmorriso at calpoly.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.02084
or
http://arXiv.org/abs/1511.02084
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jindrich Lechner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:33:22 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "1-Grothendieck $C(K)$ spaces"
by Jindrich Lechner.
Abstract:
A Banach space is said to be Grothendieck if weak and weak$^*$
convergent sequences in the dual space coincide. This notion has been
quantificated by H. Bendov\'{a}. She has proved that $\ell_\infty$ has
the quantitative Grothendieck property, namely, it is 1-Grothendieck. Our
aim is to show that Banach spaces from a certain wider class are
1-Grothendieck, precisely, $C(K)$ is 1-Grothendieck provided $K$ is
a totally disconnected compact space such that its algebra of clopen
subsets has the so called Subsequential completeness property.
Archive classification: math.FA
Submitted from: jindrich.lechner at seznam.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.02202
or
http://arXiv.org/abs/1511.02202
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by O. Delgado and E.A. Sanchez Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:38:18 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Optimal domain of $q$-concave
operators and vector measure representation of $q$-concave Banach
lattices" by O. Delgado and E.A. Sanchez Perez.
Abstract:
Given a Banach space valued $q$-concave linear operator $T$ defined on a
$\sigma$-order continuous quasi-Banach function space, we provide a
description of the optimal domain of $T$ preserving $q$-concavity, that
is, the largest $\sigma$-order continuous quasi-Banach function space
to which $T$ can be extended as a $q$-concave operator. We show in this
way the existence of maximal extensions for $q$-concave operators. As
an application, we show a representation theorem for $q$-concave Banach
lattices through spaces of integrable functions with respect to a vector
measure. This result culminates a series of representation theorems for
Banach lattices using vector measures that have been obtained in the
last twenty years.
Archive classification: math.FA
Mathematics Subject Classification: 47B38, 46G10, 46E30, 46B42
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/1511.02337
or
http://arXiv.org/abs/1511.02337
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geraldo Botelho and Ewerton R. Torres
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:39:35 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Constructing hyper-ideals of
multilinear operators between Banach" by Geraldo Botelho and Ewerton
R. Torres.
Abstract:
In view of the fact that some classical methods to construct
multi-ideals fail in constructing hyper-ideals, in this paper we develop
two new methods to construct hyper-ideals of multilinear operators
between Banach spaces. These methods generate new classes of multilinear
operators and show that some important well studied classes are Banach
or p-Banach hyper-ideals.
Archive classification: math.FA
Submitted from: botelho at ufu.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.03097
or
http://arXiv.org/abs/1511.03097
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christos Saroglou and Artem Zvavitch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Nov 2015 12:41:03 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Iterations of the projection
body operator and a remark on Petty's conjectured projection inequality"
by Christos Saroglou and Artem Zvavitch.
Abstract:
We prove that if a convex body has absolutely continuous surface area
measure, whose density is sufficiently close to the constant, then
the sequence $\{\Pi^mK\}$ of convex bodies converges to the ball with
respect to the Banach-Mazur distance, as $m\rightarrow\infty$. Here,
$\Pi$ denotes the projection body operator. Our result allows us to show
that the ellipsoid is a local solution to the conjectured inequality of
Petty and to improve a related inequality of Lutwak.
Archive classification: math.MG math.FA
Remarks: 13 pages
Submitted from: csaroglo at kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.03381
or
http://arXiv.org/abs/1511.03381
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michal Kraus
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:28:25 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Quantitative coarse embeddings
of quasi-Banach spaces into a Hilbert space" by Michal Kraus.
Abstract:
We study how well a quasi-Banach space can be coarsely embedded into a
Hilbert space. Given any quasi-Banach space X which coarsely embeds into
a Hilbert space, we compute its Hilbert space compression exponent. We
also show that the Hilbert space compression exponent of X is equal to the
supremum of the amounts of snowflakings of X which admit a bi-Lipschitz
embedding into a Hilbert space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46A16, 51F99, 46B85
Remarks: 11 pages
Submitted from: mkraus at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.05214
or
http://arXiv.org/abs/1511.05214
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephane Chretien
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:29:59 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On the restricted invertibility
problem with an additional constraint for random matrices" by Stephane
Chretien.
Abstract:
The Restricted Invertibility problem is the problem of selecting the
largest subset of columns of a given matrix $X$, while keeping the
smallest singular value of the extracted submatrix above a certain
threshold. In this paper, we address this problem in the simpler case
where $X$ is a random matrix but with the additional constraint that the
selected columns be almost orthogonal to a given vector $v$. Our main
result is a lower bound on the number of columns we can extract from a
normalized i.i.d. Gaussian matrix for the worst $v$.
Archive classification: math.PR math.FA
Submitted from: stephane.chretien at npl.co.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.05463
or
http://arXiv.org/abs/1511.05463
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo, Wilson Cuellar,
Valentin Ferenczi, and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:32:06 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Complex structures on twisted
Hilbert spaces" by Jesus M. F. Castillo, Wilson Cuellar, Valentin
Ferenczi, and Yolanda Moreno.
Abstract:
We investigate complex structures on twisted Hilbert spaces, with
special attention paid to the Kalton-Peck $Z_2$ space and to the
hyperplane problem. We consider (nontrivial) twisted Hilbert spaces
generated by centralizers obtained from an interpolation scale of K\"othe
function spaces. We show there are always complex structures on the
Hilbert space that cannot be extended to the twisted Hilbert space. If,
however, the scale is formed by rearrangement invariant K\"othe function
spaces then there are complex structures on it that can be extended to a
complex structure of the twisted Hilbert space. Regarding the hyperplane
problem we show that no complex structure on $\ell_2$ can be extended
to a complex structure on an hyperplane of $Z_2$ containing it.
Archive classification: math.FA
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.05867
or
http://arXiv.org/abs/1511.05867
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peter G. Casazza, Daniel Freeman, and
Richard G. Lynch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:33:40 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Weaving Schauder frames" by Peter
G. Casazza, Daniel Freeman, and Richard G. Lynch.
Abstract:
We extend the concept of weaving Hilbert space frames to the Banach
space setting. Similar to frames in a Hilbert space, we show that for
any two approximate Schauder frames for a Banach space, every weaving
is an approximate Schauder frame if and only if there is a uniform
constant $C\geq 1$ such that every weaving is a $C$-approximate Schauder
frame. We also study weaving Schauder bases, where it is necessary
to introduce two notions of weaving. On one hand, we can ask if two
Schauder bases are woven when considered as Schauder frames with their
biorthogonal functionals, and alternatively, we can ask if each weaving
of two Schauder bases remains a Schauder basis. We will prove that these
two notions coincide when all weavings are unconditional, but otherwise
they can be different. Lastly, we prove two perturbation theorems for
approximate Schauder frames.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 42C15
Submitted from: rilynch37 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.06093
or
http://arXiv.org/abs/1511.06093
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Draga and Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:35:50 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Direct sums and summability of
the Szlenk index" by Szymon Draga and Tomasz Kochanek.
Abstract:
We prove that the $c_0$-sum of separable Banach spaces with uniformly
summable Szlenk index has summable Szlenk index, whereas this result is
no longer valid for more general direct sums. We also give a formula
for the Szlenk power type of the ð-direct sum of separable
spaces provided
that ð has a shrinking unconditional basis whose dual basis
yields an
asymptotic ℓp structure in ð∗. As a corollary, we show that the
Tsirelson
direct sum of infinitely many copies of c0 has power type 1 but
non-summable Szlenk index.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B20
Remarks: 26 pp
Submitted from: t_kochanek at wp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.07632
or
http://arXiv.org/abs/1511.07632
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexandru Aleman and Laurian Suciu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Dec 2015 13:37:28 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "On ergodic operator means in
Banach spaces" by Alexandru Aleman and Laurian Suciu.
Abstract:
We consider a large class of operator means and prove that a number of
ergodic theorems, as well as growth estimates known for particular cases,
continue to hold in the general context under fairly mild regularity
conditions. The methods developed in the paper not only yield a new
approach based on a general point of view, but also lead to results that
are new, even in the context of the classical Cesaro means.
Archive classification: math.FA
Submitted from: laurians2002 at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1511.08929
or
http://arXiv.org/abs/1511.08929
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez Perez,
and Abraham Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 13:25:59 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Some results on almost square
Banach spaces" by Julio Becerra Guerrero, Gines Lopez Perez, and Abraham
Rueda.
Abstract:
We study almost square Banach spaces under a topological point of view.
Indeed, we prove that the class of Banach spaces which admits an
equivalent norm to be ASQ is that of those Banach spaces which contain
an isomorphic copy of $c_0$. We also prove that the symmetric projective
tensor products of an almost square Banach space have the strong diameter
two property
Archive classification: math.FA
Remarks: 12 pages
Submitted from: arz0001 at correo.ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.00610
or
http://arXiv.org/abs/1512.00610
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Matthieu Fradelizi, Mokshay Madiman, Arnaud
Marsiglietti, and Artem Zvavitch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 13:57:08 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Do Minkowski averages get
progressively more convex?" by Matthieu Fradelizi, Mokshay Madiman,
Arnaud Marsiglietti, and Artem Zvavitch.
Abstract:
Let us define, for a compact set $A \subset \mathbb{R}^n$, the Minkowski
averages of $A$: $$ A(k) =3D \left\{\frac{a_1+\cdots +a_k}{k}
: a_1, \ldo= ts, a_k\in A\right\}=3D\frac{1}{k}\Big(\underset{k\
{\rm times}}{\underbrace{= A + \cdots + A}}\Big). $$ We study the
monotonicity of the convergence of $A(= k)$ towards the convex hull
of $A$, when considering the Hausdorff distance, the volume deficit
and a non-convexity index of Schneider as measures of convergence. For
the volume deficit, we show that monotonicity fails in general, thus
disproving a conjecture of Bobkov, Madiman and Wang. For Schneider's
non-convexity index, we prove that a strong form of monotonic= ity
holds, and for the Hausdorff distance, we establish that the sequence
is eventually nonincreasing.
Archive classification: math.FA math.OC
Remarks: 6 pages, including figures. Contains announcement of results th=
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.03718
or
http://arXiv.org/abs/1512.03718
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mathieu Meyer and Shlomo Reisner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 13:58:42 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "The isotropy constant and boundary
properties of convex bodies" by Mathieu Meyer and Shlomo Reisner.
Abstract:
Let ${\cal K}^n$ be the set of all convex bodies in $\mathbb R^n$ endo=
wed with the Hausdorff distance. We prove that if $K\in {\cal K}^n$ has
posit= ive generalized Gauss curvature at some point of its boundary,
then $K$ is no= t a local maximizer for the isotropy constant $L_K$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 52A20, 53A05
Submitted from: reisner at math.haifa.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.02927
or
http://arXiv.org/abs/1512.02927
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guillermo P. Curbera and Werner J. Ricker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:03:09 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Abstract Ces\`aro spaces: Integral
representations" by Guillermo P. Curbera and Werner J. Ricker.
Abstract:
The Ces\`aro function spaces $Ces_p=[C,L^p]$, $1\le p\le\infty$, have
received renewed attention in recent years. Many properties of $[C,L^p]$
are known. Less is known about $[C,X]$ when the Ces\`aro operator
takes its values in a rearrangement invariant (r.i.) space $X$ other
than $L^p$. In this paper we study the spaces $[C,X]$ via the methods
of vector measures and vector integration. These techniques allow us
to identify the absolutely continuous part of $[C,X]$ and the Fatou
completion of $[C,X]$; to show that $[C,X]$ is never reflexive and
never r.i.; to identify when $[C,X]$ is weakly sequentially complete,
when it is isomorphic to an AL-space, and when it has the Dunford-Pettis
property. The same techniques are used to analyze the operator $C:[C,X]\to
X$; it is never compact but, it can be completely continuous.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46G10
Remarks: 21 pages
Submitted from: curbera at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.02760
or
http://arXiv.org/abs/1512.02760
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bruno de Mendonca Braga
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:06:36 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Coarse and uniform embeddings"
by Bruno de Mendonca Braga.
Abstract:
In these notes, we study the relation between uniform and coarse embed=
dings between Banach spaces. In order to understand this relation
better, we al= so look at the problem of when a coarse embedding can
be assumed to be topological. Among other results, we show that if
a Banach space $X$ uniformly embeds into a minimal Banach space $Y$,
then $X$ simultaneously coarsely and uniformly embeds into $Y$, and
if a Banach space $X$ coarsely embeds into a minimal Banach space $Y$,
then $X$ simultaneously coarsely and homeomorphically embeds into $Y$
by a map with uniformly continuous inverse.
Archive classification: math.FA
Mathematics Subject Classification: 46B80
Submitted from: demendoncabraga at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.03109
or
http://arXiv.org/abs/1512.03109
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey V. Astashkin, Karol Lesnik, and Lech
Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:11:25 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Isomorphic structure of Ces\`aro
and Tandori spaces" by Sergey V. Astashkin, Karol Lesnik, and Lech
Maligranda.
Abstract:
We investigate the isomorphic structure of the Ces\`aro spaces and their
duals, the Tandori spaces. The main result states that the
Ces\`aro function space $Ces_{\infty}$ and its sequence counterpart
$ces_{\infty}$ are isomorphic, which answers to the question posted in
\cite{AM09}. This is rather surprising since $Ces_{\infty}$ has no
natural lattice predual similarly as the known Talagrand's example
\cite{Ta81}. We prove that neither $ces_{\infty}$ is isomorphic
to $l_{\infty}$ nor $Ces_{\infty}$ is isomorphic to the Tandori space
$\widetilde{L_1}$ with the norm $\|f\|_{\widetilde{L_1}}
=\|\widetilde{f}\|_{L_1},$ where $\widetilde{f}(t): \esssup_{s \geq t}
|f(s)|.$ Our investigation involves also an examination of the Schur
and Dunford-Pettis properties of Ces\`aro and Tandori spaces. In
particular, using Bourgain's results we show that a wide class of
Ces{\`a}ro-Marcinkiewicz and Ces{\`a}ro-Lorentz spaces have the latter
property.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.03336
or
http://arXiv.org/abs/1512.03336
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez,
and Abraham Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:14:13 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Octahedrality in Lipschitz
free Banach spaces" by Julio Becerra Guerrero, Gines Lopez-Perez, and
Abraham Rueda.
Abstract:
The aim of this note is to study octahedrality in vector valued
Lipschitz-free Banach spaces on a metric space under topological
hypotheses on it. As a consequence, we get that the space of Lipschitz
functions on a metric space valued in a dual Banach space satisfies
the weak-star strong diameter two property, under natural topological
hipothesess on the metric space. Also, we show an example proving that
these hypotheses are optimal.
Archive classification: math.FA
Remarks: 18 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/1512.03558
or
http://arXiv.org/abs/1512.03558
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Aicke Hinrichs, Anton Kolleck, and Jan
Vybiral
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:15:50 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Carl's inequality for quasi-Banach
spaces" by Aicke Hinrichs, Anton Kolleck, and Jan Vybiral.
Abstract:
We prove that for any two quasi-Banach spaces $X$ and $Y$ and any
$\alpha>0$ there exists a constant $c_\alpha>0$ such that $$ \sup_{1\le
k\le n}k^{\alpha}e_k(T)\le c_\alpha \sup_{1\le k\le n} k^\alpha c_k(T)
$$ holds for all linear and bounded operators $T:X\to Y$. Here $e_k(T)$
is the $k$-th entropy number of $T$ and $c_k(T)$ is the $k$-th Gelfand
number of $T$. For Banach spaces $X$ and $Y$ this inequality is widely
used and well-known as Carl's inequality. For general quasi-Banach spaces
it is a new result, which closes a gap in the argument of Donoho in his
seminal paper on compressed sensing.
Archive classification: math.FA
Remarks: 12 pages
Submitted from: aicke.hinrichs at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.04421
or
http://arXiv.org/abs/1512.04421
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geraldo Botelho, Jamilson R. Campos, and
Joedson Santos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:17:47 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Operator ideals related to
absolutely summing and Cohen strongly operators" by Geraldo Botelho,
Jamilson R. Campos, and Joedson Santos.
Abstract:
We study the ideals of linear operators between Banach spaces determined
by the transformation of vector-valued sequences involving the new
sequence space introduced by Karn and Sinha \cite{karnsinha} and the
classical spaces of absolutely, weakly and Cohen strongly summable
sequences. As applications, we prove a new factorization theorem for
absolutely summing operators and a contribution to the existence of
infinite dimensional spaces formed by non-absolutely summing operators
is given.
Archive classification: math.FA
Mathematics Subject Classification: 46B45, 47B10, 47L20
Remarks: 15 pages
Submitted from: jamilson at dce.ufpb.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.04713
or
http://arXiv.org/abs/1512.04713
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Paul F.X. Muller and Johanna Penteker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Dec 2015 14:19:31 -0600 (CST)
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
This is an announcement for the paper "Absolutely summing operators and
atomic decomposition in bi-parameter Hardy spaces" by Paul F.X. Muller
and Johanna Penteker.
Abstract:
For $f \in H^p(\delta^2)$, $0<p\leq 2$, with Haar expansion $f=\sum f_{I
\times J}h_{I\times J}$ we constructively determine the Pietsch measure
of the $2$-summing multiplication operator
\[\mathcal{M}_f:\ell^{\infty} \rightarrow H^p(\delta^2), \quad
(\varphi_{I\times J}) \mapsto \sum \varphi_{I\times J}f_{I \times
J}h_{I \times J}. \] Our method yields a constructive proof of Pisier's
decomposition of $f \in H^p(\delta^2)$
\[|f|=|x|^{1-\theta}|y|^{\theta}\quad\quad \text{ and }\quad\quad
\|x\|_{X_0}^{1-\theta}\|y\|^{\theta}_{H^2(\delta^2)}\leq
C\|f\|_{H^p(\delta^2)}, \] where $X_0$ is Pisier's extrapolation lattice
associated to $H^p(\delta^2)$ and $H^2(\delta^2)$. Our construction
of the Pietsch measure for the multiplication operator $\mathcal{M}_f$
involves the Haar coefficients of $f$ and its atomic decomposition. We
treated the one-parameter $H^p$-spaces in [P.F.X M\"uller, J.Penteker,
$p$-summing multiplication operators, dyadic Hardy spaces and atomic
decomposition, Houston Journal Math.,41(2):639-668,2015.].
Archive classification: math.FA
Mathematics Subject Classification: 42B30 46B25 46B09 46B42 46E40
47B10 60G42
Remarks: 10 pages
Submitted from: johanna.penteker at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.04790
or
http://arXiv.org/abs/1512.04790
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:28:26 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Jesus A. Jaramillo, Raquel Gonzalo and
Diego Yanez
This is an announcement for the paper "Asymptotic Smoothness, Convex
Envelopes and Polynomial Norms" by Jesus A. Jaramillo, Raquel Gonzalo
and Diego Yanez.
Abstract:
We introduce a suitable notion of asymptotic smoothness on infinite
dimensional Banach spaces, and we prove that, under some structural
restrictions on the space, the convex envelope of an asymptotically smooth
function is asymptotically smooth. Furthermore, we study convexity and
smoothness properties of polynomial norms, and we obtain that a polynomial
norm of degree N has modulus of convexity of power type N.
Archive classification: math.FA
Submitted from: jaramil at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.05407
or
http://arXiv.org/abs/1512.05407
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:30:50 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Guillermo P. Curbera and Werner J. Ricker
This is an announcement for the paper "The weak Banach-Saks property
for function spaces" by Guillermo P. Curbera and Werner J. Ricker.
Abstract:
We establish the weak Banach-Saks property for function spaces arising
as the optimal domain of an operator.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46G10
Submitted from: curbera at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.05728
or
http://arXiv.org/abs/1512.05728
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:35:01 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Siu Lam Leung, Sarah Nelson, Sofiya
Ostrovska, and Mikhail Ostrovskii
This is an announcement for the paper "Distortion of embeddings of
binary trees into diamond graphs" by Siu Lam Leung, Sarah Nelson, Sofiya
Ostrovska, and Mikhail Ostrovskii.
Abstract:
Diamond graphs and binary trees are important examples in the theory of
metri
c embeddings and also in the theory of metric characterizations
of Banach spaces. Some results for these families of graphs are
parallel to each other, for example superreflexivity of Banach spaces
can be characterized both in terms of binary trees (Bourgain, 1986)
and diamond graphs (Johnson-Schechtman, 2009). In this connection,
it is natural to ask whether one of these families admits uniformly
bilipschitz embeddings into the other. This question was answered in
the negative by Ostrovskii (2014), who left it open to determine the order
of growth of the distortions. The main purpose of this paper is to get a
sharp-up-to-a-logarithmic-factor estimate for the distortions of embeddings
of binary trees into diamond graphs.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 05C12, 30L05, 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/1512.06438
or
http://arXiv.org/abs/1512.06438
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:39:42 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Sofiya Ostrovska and Mikhail I. Ostrovskii
This is an announcement for the paper "Nonexistence of embeddings with
uniformly bounded distortions of Laakso graphs into diamond graphs"
by Sofiya Ostrovska and Mikhail I. Ostrovskii.
Abstract:
Diamond graphs and Laakso graphs are important examples in the theory
of metric embeddings. Many results for these families of graphs are
similar to each other. In this connection, it is natural to ask whether
one of these families admits uniformly bilipschitz embeddings into the
other. The well-known fact that Laakso graphs are uniformly doubling
but diamond graphs are not, immediately implies that diamond graphs do
not admit uniformly bilipschitz embeddings into Laakso graphs. The main
goal of this paper is to prove that Laakso graphs do not admit uniformly
bilipschitz embeddings into diamond graphs.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 05C12, 30L05, 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/1512.06439
or
http://arXiv.org/abs/1512.06439
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:46:57 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Stephen Simons
This is an announcement for the paper "Bootstrapping the
Mazur--Orlicz--K\"onig theorem" by Stephen Simons.
Abstract:
In this paper, we give some extensions of K\"onig's extension of the
Mazur-Orlicz theorem. These extensions include generalizations of a
surprising recent result of Sun Chuanfeng, and generalizations to the
product of more than two spaces of the ``Hahn-Banach-Lagrange'' theorem.
Archive classification: math.FA
Mathematics Subject Classification: 46A22, 46N10
Remarks: 9 pages
Submitted from: stesim38 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.08020
or
http://arXiv.org/abs/1512.08020
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:49:08 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Giorgos Chasapis, Apostolos Giannopoulos
and Dimitris-Marios Liakopoulos
This is an announcement for the paper "Estimates for measures of lower
dimensional sections of convex bodies" by Giorgos Chasapis, Apostolos
Giannopoulos and Dimitris-Marios Liakopoulos.
Abstract:
We present an alternative approach to some results of Koldobsky on
measures of sections of symmetric convex bodies, which allows us to extend
them to the not necessarily symmetric setting. We prove that if $K$ is
a convex body in ${\mathbb R}^n$ with $0\in {\rm int}(K)$ and if $\mu $
is a measure on ${\mathbb R}^n$ with a locally integrable non-negative
density $g$ on ${\mathbb R}^n$, then \begin{equation*}\mu (K)\leq
\left (c\sqrt{n-k}\right )^k\max_{F\in G_{n,n-k}}\mu (K\cap F)\cdot
|K|^{\frac{k}{n}}\end{equation*} for every $1\leq k\leq n-1$. Also,
if $\mu $ is even and log-concave, and if $K$ is a symmetric convex
body in ${\mathbb R}^n$ and $D$ is a compact subset of ${\mathbb R}^n$
such that $\mu (K\cap F)\leq \mu (D\cap F)$ for all $F\in G_{n,n-k}$,
then \begin{equation*}\mu (K)\leq \left (ckL_{n-k}\right )^{k}\mu
(D),\end{equation*} where $L_s$ is the maximal isotropic constant of
a convex body in ${\mathbb R}^s$. Our method employs a generalized
Blaschke-Petkantschin formula and estimates for the dual affine
quermassintegrals.
Archive classification: math.MG math.FA
Submitted from: gchasapis at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.08393
or
http://arXiv.org/abs/1512.08393
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:52:43 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Antonio Aviles, Antonio J. Guirao,
Sebastian Lajara, Jose Rodriguez, and Pedro Tradacete
This is an announcement for the paper "Weakly compactly generated Banach
lattices" by Antonio Aviles, Antonio J. Guirao, Sebastian Lajara, Jose
Rodriguez, and Pedro Tradacete.
Abstract:
We study the different ways in which a weakly compact set can generate a
Banach lattice. Among other things, it is shown that in an order
continuous Banach lattice $X$, the existence of a weakly compact set
$K \subset X$ such that $X$ coincides with the band generated by $K$,
implies that $X$ is WCG.
Archive classification: math.FA
Mathematics Subject Classification: 46B42, 46B50
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.08628
or
http://arXiv.org/abs/1512.08628
Return-path: <alspach at math.okstate.edu>
Date: Sun, 03 Jan 2016 17:54:55 -0600
To: <banach at mathdept.okstate.edu>, <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Karim Khanaki
This is an announcement for the paper "Correspondences between model
theory and banach space theory" by Karim Khanaki.
Abstract:
In \cite{K3} we pointed out the correspondence between a result
of Shelah in model theory, i.e. a theory is unstable if and only if
it has IP or SOP, and the well known compactness theorem of Eberlein
and \v{S}mulian in functional analysis. In this paper, we relate a
{\em natural} Banach space $V$ to a formula $\phi(x,y)$, and show that
$\phi$ is stable (resp NIP, NSOP) if and only if $V$ is reflexive (resp
Rosenthal, weakly sequentially complete) Banach space. Also, we present
a proof of the Eberlein-\v{S}mulian theorem by a model theoretic approach
using Ramsey theorems which is illustrative to show some correspondences
between model theory and Banach space theory.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 03C45, 46E15, 46B50
Submitted from: khanaki at ipm.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1512.08691
or
http://arXiv.org/abs/1512.08691
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