February 2015 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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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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