June 2015 - Banach - mathdept.okstate.edu

Abstract of a paper by Trond A. Abrahamsen, Peter Hajek, Olav Nygaard, Jarno Talponen, and Stanimir Troyanski
by alspach＠math.okstate.edu 29 Jun '15

29 Jun '15

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(a)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

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Abstract of a paper by Assaf Naor and Yuval Rabani
by alspach＠math.okstate.edu 29 Jun '15

29 Jun '15

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(a)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

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Abstract of a paper by Van Hoang Nguyen
by alspach＠math.okstate.edu 29 Jun '15

29 Jun '15

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(a)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

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SUMIRFAS 2015
by Bill Johnson 26 Jun '15

26 Jun '15

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>.

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Abstract of a paper by F. Albiac and J. L. Ansorena
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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Abstract of a paper by Umut Caglar and Deping Ye
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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Abstract of a paper by Apoorva Khare and Bala Rajaratnam
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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Abstract of a paper by Claudia Correa and Daniel V. Tausk
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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Abstract of a paper by Y. Estaremi, S. Maghsodi and I. Rahmani
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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Abstract of a paper by J. L. Ansorena, F. Albiac, S. J. Dilworth and Denka Kutzarova
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

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(a)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

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