November 2013 - 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 Antonin Prochazka and Luis Sanchez-Gonzalez
by alspach＠math.okstate.edu 11 Dec '13

11 Dec '13

This is an announcement for the paper "Low distortion embeddings into Asplund Banach spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez. Abstract: We give a simple example of a countable metric space that does not embed bi-Lipschitz with distortion strictly less than 2 into any Asplund space. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B85 Remarks: 3 pages Submitted from: antonin.prochazka(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.4584 or http://arXiv.org/abs/1311.4584

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Abstract of a paper by Christos Saroglou
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "On the equivalence between two problems of asymmetry on convex bodies" by Christos Saroglou. Abstract: The simplex was conjectured to be the extremal convex body for the two following ``problems of asymmetry'':\\ P1) What is the minimal possible value of the quantity $\max_{K'} |K'|/|K|$? Here, $K'$ ranges over all symmetric convex bodies contained in $K$.\\ P2) What is the maximal possible volume of the Blaschke-body of a convex body of volume 1?\\ Our main result states that (P1) and (P2) admit precisely the same solutions. This complements a result from [{\rm K. B\"{o}r\"{o}czky, I. B\'{a}r\'{a}ny, E. Makai Jr. and J. Pach}, Maximal volume enclosed by plates and proof of the chessboard conjecture], Discrete Math. {\bf 69} (1986), 101--120], stating that if the simplex solves (P1) then the simplex solves (P2) as well. Archive classification: math.FA Remarks: Submitted for publication, November 2013 Submitted from: saroglou(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.4955 or http://arXiv.org/abs/1311.4955

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Abstract of a paper by Christos Saroglou
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Remarks on the conjectured log-Brunn-Minkowski inequality" by Christos Saroglou. Abstract: \footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality together with its equality cases for pairs of unconditional convex bodies with respect to the same orthonormal basis. Applications of this fact are discussed. Moreover, we prove that the log-Brunn-Minkowski inequality is equivalent to the (B)-Theorem for the uniform measure of the cube (this has been proven by Cordero-Erasquin, Fradelizi and Maurey for the gaussian measure instead). Archive classification: math.FA Remarks: Submitted 30 April,2013 Submitted from: saroglou(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.4954 or http://arXiv.org/abs/1311.4954

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Abstract of a paper by Daniel Pellegrino, Pilar Rueda, and Enrique A. Sanchez-Perez
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Weak compactness and strongly summing multilinear operators" by Daniel Pellegrino, Pilar Rueda, and Enrique A. Sanchez-Perez. Abstract: Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials { one of the most natural extensions of the linear case to the non linear framework { weak compactness does not hold in general. We show that a subclass of the class of strongly summing multilinear operators/polynomials, sharing its main properties such as Grothendieck's Theorem, Pietsch Domination Theorem and Dvoretzky{Rogers Theorem, has even better properties like weak compactness and a natural factorization theorem. Archive classification: math.FA Mathematics Subject Classification: 46A32 Submitted from: pilar.rueda(a)uv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.4685 or http://arXiv.org/abs/1311.4685

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Abstract of a paper by Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen Kudaybergenov
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Geometric characterization of $L_1$-spaces" by Normuxammad Yadgorov, Mukhtar Ibragimov, and Karimbergen Kudaybergenov. Abstract: The paper is devoted to a description of all strongly facially symmetric spaces which are isometrically isomorphic to $L_1$-spaces. We prove that if $Z$ is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of $Z$ is unitary then, the space $Z$ is isometrically isomorphic to the space $L_1(\Omega, \Sigma, \mu),$ where $(\Omega, \Sigma, \mu)$ is an appropriate measure space having the direct sum property. Archive classification: math.OA Mathematics Subject Classification: 46B20 Remarks: Accepted to publication in the journal Studia Mathematica Submitted from: karim20061(a)yandex.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.4429 or http://arXiv.org/abs/1311.4429

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Abstract of a paper by Dario Cordero-Erausquin, Matthieu Fradelizi, Grigoris Paouris, and Peter Pivovarov
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Volume of the polar of random sets and shadow systems" by Dario Cordero-Erausquin, Matthieu Fradelizi, Grigoris Paouris, and Peter Pivovarov. Abstract: We obtain optimal inequalities for the volume of the polar of random sets, generated for instance by the convex hull of independent random vectors in Euclidean space. Extremizers are given by random vectors uniformly distributed in Euclidean balls. This provides a random extension of the Blaschke-Santalo inequality which, in turn, can be derived by the law of large numbers. The method involves generalized shadow systems, their connection to Busemann type inequalities, and how they interact with functional rearrangement inequalities. Archive classification: math.FA Submitted from: pivovarovp(a)missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.3690 or http://arXiv.org/abs/1311.3690

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Abstract of a paper by Nacib Albuquerque, Frederic Bayart, Daniel Pellegrino, and Seoane Sepulveda
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators" by Nacib Albuquerque, Frederic Bayart, Daniel Pellegrino, and Seoane Sepulveda. Abstract: In this paper we obtain quite general forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simple and straightforward proofs. The technique used is a very recent interpolative approach; this method is also used in this paper to obtain better constants for vector-valued Bohnenblust-Hille type inequalities. Archive classification: math.FA Remarks: 7 pages Submitted from: jseoane(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.3177 or http://arXiv.org/abs/1311.3177

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Abstract of a paper by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Domination by positive weak* Dunford-Pettis operators on Banach" by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji. Abstract: Recently, J. H'michane et al. introduced the class of weak* Dunford-Pettis operators on Banach spaces, that is, operators which send weakly compact sets onto limited sets. In this paper the domination problem for weak* Dunford-Pettis operators is considered. Let $S, T:E\rightarrow F$ be two positive operators between Banach lattices $E$ and $F$ such that $0\leq S\leq T$. We show that if $T$ is a weak$^{*}$ Dunford-Pettis operator and $F$ is $\sigma$-Dedekind complete, then $S$ itself is weak* Dunford-Pettis. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65 Remarks: 8 pages Submitted from: jinxichen(a)home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.2808 or http://arXiv.org/abs/1311.2808

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Abstract of a paper by Jean Bourgain and Jelani Nelson
by alspach＠math.okstate.edu 22 Nov '13

22 Nov '13

This is an announcement for the paper "Toward a unified theory of sparse dimensionality reduction in Euclidean space" by Jean Bourgain and Jelani Nelson. Abstract: Let $\Phi\in\mathbb{R}^{m\times n}$ be a sparse Johnson-Lindenstrauss transform [Kane, Nelson, SODA 2012] with $s$ non-zeroes per column. For $T$ a subset of the unit sphere, $\varepsilon\in(0,1/2)$ given, we study settings for $m,s$ required to ensure $$ \mathop{\mathbb{E}}_\Phi \sup_{x\in T} \left|\|\Phi x\|_2^2 - 1 \right| < \varepsilon , $$ i.e. so that $\Phi$ preserves the norm of every $x\in T$ simultaneously and multiplicatively up to $1+\varepsilon$. In particular, our most general theorem shows that it suffices to set $m = \tilde{\Omega}(\gamma_2^2(T) + 1)$ and $s = \tilde{\Omega}(1)$ as long as $s,m$ additionally satisfy a certain tradeoff condition that is governed by the geometry of $T$ (and as we show for several examples of interest, is easy to verify). Here $\gamma_2$ is Talagrand's functional, and we write $f = \tilde{\Omega}(g)$ to mean $f \ge Cg (\varepsilon^{-1}\log n)^c$ for some constants $C,c>0$. Our result can be seen as an extension to sparse $\Phi$ of works of [Klartag, Mendelson, J. Funct. Anal. 2005], [Gordon, GAFA 1988], and [Mendelson, Pajor, Tomczak-Jaegermann, GAFA 2007], which were concerned with dense $\Phi$ having i.i.d. (sub)gaussian entries. Our work introduces a theory that qualitatively unifies several results related to the Johnson-Lindenstrauss lemma, subspace embeddings, and Fourier-based methods for obtaining matrices satisfying the restricted isometry property. Archive classification: cs.DS cs.CG cs.IT math.FA math.IT math.PR Submitted from: minilek(a)seas.harvard.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.2542 or http://arXiv.org/abs/1311.2542

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