Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Amir Livne Bar-on
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "The (B) conjecture for uniform measures in the plane" by Amir Livne Bar-on. Abstract: We prove that for any two centrally-symmetric convex shapes $K,L \subset \mathbb{R}^2$, the function $t \mapsto |e^t K \cap L|$ is log-concave. This extends a result of Cordero-Erausquin, Fradelizi and Maurey in the two dimensional case. Possible relaxations of the condition of symmetry are discussed. Archive classification: math.FA Remarks: 10 pages Submitted from: livnebaron(a)mail.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.6584 or http://arXiv.org/abs/1311.6584

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School and conference announcement: Besancon, Autumn 2014
by glancien＠math.cnrs.fr 16 Dec '13

16 Dec '13

Dear colleagues, As part of the trimester on "Geometric and noncommutative methods in functional analysis" organized by the "Laboratoire de Mathematiques de Besancon" during the Autumn 2014, we wish to announce the two following events. 1) The Autum school on "Nonlinear geometry of Banach spaces and applications", in Metabief (October 20-24, 2014). The following mathematicians have kindly accepted our invitation to deliver a short course: Gilles Godefroy (Université Paris 6), Petr Hajek (Czech Academy of Sciences and Czech Technical University), Manor Mendel (Open University of Israel - to be confirmed), Nirina Lovasoa Randrianarivony (Saint Louis University - to be confirmed), Guoliang Yu (Texas A&M University). 2) The conference on "Geometric functional analysis and its applications" in Besancon (October 27-31, 2014). The following main speakers have already agreed to deliver a plenary lecture: Fernando Albiac (Univ. Publica de Navarra), Florent Baudier (Texas A&M University, Paris 6) , Robert Deville (Univ. Bordeaux) , Stephen Dilworth (Univ. South Carolina), Valentin Ferenczi (Univ. Sao Paulo) , Bill Johnson (Texas A&M University), Beata Randrianantoanina (Miami Univ Ohio), Gideon Schechtman (Weizmann Institute), Thomas Schlumprecht (Texas A&M University), Alain Valette (Univ. Neuchatel). Other participants will have the opportunity to give a short talk. The purpose of these meetings is to bring together researchers and students with common interest in the field. They will offer many possibilities for informal discussions. Graduate students and others beginning their mathematical career are encouraged to participate. You can visit the following websites: trimester: http://trimestres-lmb.univ-fcomte.fr/af.html School in Metabief: https://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=… Conference in Besancon: https://trimestres-lmb.univ-fcomte.fr/Conference-on-Geometric-Functional.ht… Registration for both events is now open. The organizers, Gilles Lancien and Tony Prochazka ----- Fin du message transféré -----

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Conference announcement: Stochastic processes and high dimensional probability distributions.
by Elizabeth Meckes 16 Dec '13

16 Dec '13

Stochastic processes and high dimensional probability distributionsJune 16 - 20, 2014Euler International Mathematical Institute, Saint-Petersburg, Russia A conference in honor of the lifelong contributions of Vladimir Nikolayevich Sudakov. The conference will focus on several closely related directions in Probability Theory and Analysis including: Geometric problems about Gaussian and other linear stochastic processes; Typical distributions, measure concentration and high dimensional phenomena; Optimal transportation and associated Sobolev-type and information-theoretic inequalities. Invited speakers are: V.Bogachev (Moscow University), A.Dembo (Stanford), R.Dudley (MIT), W.Gangbo (Georgia Tech), N.Gozlan (Paris-Est), I.Ibragimov (Steklov Institute), S.Kwapien (Warsaw), R Latala (Warsaw), M.Ledoux (Toulouse), R.McCann (Toronto), M.Milman (Florida), V.Milman (Tel Aviv), H. von Weizs\"acker (Kaiserslautern). There will be an opportunity for contributed talks. A preliminary web page for the conference can be found at http://www.pdmi.ras.ru/EIMI/2014/Sppd/index.html We are applying for NSF support for travel for US participants; priority will be given to young researchers (especially students and post-docs) without other sources of support. -- Elizabeth S. Meckes Associate Professor of Mathematics Case Western Reserve University

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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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meeting
by Gonzalez Ortiz, Manuel 03 Dec '13

03 Dec '13

This is an announcement of the Meeting INTERPOLATION AND BANACH SPACE CONSTRUCTIONS Castro Urdiales, Cantabria, Spain 2nd–6th June 2014 This Meeting is focused on the topics of interpolation theory, Banach space constructions and the interplay between them, and is aimed at researchers in Banach space theory. It will consist of invited talks, short communications and discussion time. Those wishing to deliver a short talk or take part in the poster session should indicate so when filling the registration form. Invited speakers include Pandelis Dodos (University of Athens), Valentin Ferenczi (Universidade de São Paulo), Piotr Koszmider (Polish Academy of Sciences/Technical University of Łódź), Jordi López Abad (Instituto de Ciencias Matemáticas) and Richard Rochberg (Washington University in St. Louis). For additional information and registration we refer to the web page of the meeting: http://www.ciem.unican.es/encuentros/banach/2014/

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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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