Banach

banach@mathdept.okstate.edu

2549 discussions

Workshop at A&M
by Bill Johnson 05 Mar '15

05 Mar '15

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(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week "From Commutators to BCP Operators", please contact Hari Bercovici <bercovic(a)indiana.edu> or Vern Paulsen <vern(a)math.uh.edu>.

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Abstract of a paper by William B. Johnson and Gideon Schechtman
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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Abstract of a paper by Miguel Martin
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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

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Abstract of a paper by Miguel Martin
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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Abstract of a paper by Jan-David Hardtke
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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Abstract of a paper by Patrick Cheridito, Michael Kupper and Ludovic Tangpi
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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Abstract of a paper by Ryan Causey
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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Abstract of a paper by Donghai Ji, Byunghoon Lee and Qingying Bu
by alspach＠math.okstate.edu 27 Feb '15

27 Feb '15

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(a)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

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CBMS conference: "Introduction to the Theory of Valuations and Convex Sets"
by Artem Zvavitch 17 Feb '15

17 Feb '15

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(a)math.kent.edu for any further information. Sincerely, The Analysis Group at Kent State University

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Abstract of a paper by Malgorzata M. Czerwinska and Anna Kaminska
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

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

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