Banach December 2013

banach@mathdept.okstate.edu

6 participants
19 discussions

Abstract of a paper by Oleg Reinov
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "On operators with bounded approximation property" by Oleg Reinov. Abstract: It is known that any separable Banach space with BAP is a complemented subspace of a Banach space with a basis. We show that every operator with bounded approximation property, acting from a separable Banach space, can be factored through a Banach space with a basis. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 5 pages Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.2116 or http://arXiv.org/abs/1312.2116

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Abstract of a paper by Daniel Carando, Daniel Galicer and Damian Pinasco
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Energy integrals and metric embedding theory" by Daniel Carando, Daniel Galicer and Damian Pinasco. Abstract: For some centrally symmetric convex bodies $K\subset \mathbb R^n$, we study the energy integral $$ \sup \int_{K} \int_{K} \|x - y\|_r^{p}\, d\mu(x) d\mu(y), $$ where the supremum runs over all finite signed Borel measures $\mu$ on $K$ of total mass one. In the case where $K = B_q^n$, the unit ball of $\ell_q^n$ (for $1 \leq q \leq 2$) or an ellipsoid, we obtain the exact value or the correct asymptotical behavior of the supremum of these integrals. We apply these results to a classical embedding problem in metric geometry. We consider in $\mathbb R^n$ the Euclidean distance $d_2$. For $0 < \alpha < 1$, we estimate the minimum $R$ for which the snowflaked metric space $(K, d_2^{\alpha})$ may be isometrically embedded on the surface of a Hilbert sphere of radius $R$. Archive classification: math.MG math.FA Mathematics Subject Classification: 51M16, 52A23, 31C45, 51K05, 54E40 Remarks: 18 pages Submitted from: dgalicer(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.0678 or http://arXiv.org/abs/1312.0678

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Abstract of a paper by Michael Kelly
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "The Blaschke-Santalo Inequality" by Michael Kelly. Abstract: The Blaschke-Santalo inequality is the assertion that the volume product of a symmetric convex body in Euclidean space is maximized by the Euclidean unit ball. In this paper we give a Fourier analytic proof of this fact. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A40 (Primary), 42A05, 42A85, 52A39, 46E22 (Secondary) Remarks: 11 pages, 4 figures Submitted from: mkelly(a)math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1312.0244 or http://arXiv.org/abs/1312.0244

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Abstract of a paper by Manaf Adnan Salah
by alspach＠math.okstate.edu 17 Dec '13

17 Dec '13

This is an announcement for the paper "Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps" by Manaf Adnan Salah. Abstract: Building upon the linear version of mixed summable sequences in arbitrary Banach spaces of A. Pietsch, we introduce a nonlinear version of his concept and study its properties. Extending previous work of J. D. Farmer, W. B. Johnson and J. A. Ch\'avez-Dom\'inguez, we define Lipschitz $\left(\mathfrak{m}^L\left(s;q\right),p\right)$ and Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing maps and establish inclusion theorems, composition theorems and several characterizations. Furthermore, we prove that the classes of Lipschitz $\left(r,\mathfrak{m}^L\left(r;r\right)\right)-$summing maps with $0<r<1$ coincide. We obtain that every Lipschitz map is Lipschitz $\left(p,\mathfrak{m}^L\left(s;q\right)\right)-$summing map with $1\leq s< p$ and $0<q\leq s$ and discuss a sufficient condition for a Lipschitz composition formula as in the linear case of A. Pietsch. Moreover, we discuss a counterexample of the nonlinear composition formula, thus solving a problem by J. D. Farmer and W. B. Johnson. Archive classification: math.FA Mathematics Subject Classification: 47L20 47B10 Submitted from: manaf-adnan.salah(a)uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1311.7575 or http://arXiv.org/abs/1311.7575

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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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Banach December 2013