Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Piotr W. Nowak
by alspach＠math.okstate.edu 23 Aug '11

23 Aug '11

This is an announcement for the paper "Poincar\'e inequalities and rigidity for actions on Banach spaces" by Piotr W. Nowak. Abstract: The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present conditions implying that every affine isometric action of a given group $G$ on a reflexive Banach space $X$ has a fixed point. This last property is a strong version of Kazhdan's property (T) and is equivalent to the fact that $H^1(G,\pi)=0$ for every isometric representation $\pi$ of $G$ on $X$. We give examples of groups for which every affine isometric action on an $L_p$ space has a fixed point for certain $p>2$, and present several applications. In particular, we give a lower bound on the conformal dimension of the boundary of a hyperbolic group in the Gromov density model. Archive classification: math.GR math.FA math.OA Submitted from: pnowak(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.1896 or http://arXiv.org/abs/1107.1896

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Registration Open: Functional Analysis Methods in Quantum Information. EMS Mathematical Weekend. October 7-9. Bilbao. Spain
by David Perez-Garcia 26 Jul '11

26 Jul '11

Dear colleague, The registration is already open for the Mathematical Weekend jointly organized by the Royal Spanish Society of Mathematics and the European Mathematical Society. You can register and find more information about the meeting in http://www.ehu.es/emsweekend/ Important data about the meeting: Dates: October 7-9, 2011 Venue: The Bizkaia Aretoa, Bilbao, Spain. Very close to the famous Guggenheim Museum. Special sessions: Groups and Representations, Symplectic Geometry, PDEs in Mechanics and Physics, Functional Analysis Methods in Quantum Information. See you there! Jesus Bastero and David Perez-Garcia (organizers of the session Functional Analysis Methods in Quantum Information)

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Functional Analysis Methods in Quantum Information. EMS Mathematical Weekend. October 7-9. Bilbao. Spain
by David Perez-Garcia 22 Jul '11

22 Jul '11

Dear colleague, As part of the commemorations of its centennial, the Royal Spanish Society of Mathematics (RSME) is organizing jointly with the European Mathematical Society (EMS) a Mathematical Weekend that will be held in Bilbao from October 7 to 9, 2011. As is usual in the EMS Mathematical Weekends, the meeting will begin on Friday afternoon and will end on Sunday at lunch time. All mathematicians, from Europe and elsewhere, are warmly invited to participate. As in previous editions of the EMS Mathematical Weekends, there will be several special sessions where some of the most prominent researchers in their fields will give a talk. In this edition, these are the four topics that have been selected for the special sessions: Groups and Representations, Symplectic Geometry, PDEs in Mechanics and Physics, and Functional Analysis Methods in Quantum Information. Related to the fourth topic, which presents the modern connections between Functional Analysis and Information Theory, Computer Science, Probability and Geometry, there will be a plenary talk and 6 invited contributions. The fact that the EMS and the RSME have included these new connections of Functional Analysis as a 'hot topic' illustrates their relevance for future research. It is hence a wonderful occasion, specially for young researchers, to assist and have contact with some leading researchers in the area. We hope to see you in Bilbao this fall. Jesus Bastero and David Perez-Garcia

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SUMIRFAS Schedule
by Dale Alspach 21 Jul '11

21 Jul '11

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Abstract of a paper by Omer Friedland and Olivier Guedon
by alspach＠math.okstate.edu 07 Jul '11

07 Jul '11

This is an announcement for the paper "Sparsity and non-Euclidean embeddings" by Omer Friedland and Olivier Guedon. Abstract: We present a relation between sparsity and non-Euclidean isomorphic embeddings. We introduce a general restricted isomorphism property and show how it enables to construct embeddings of $\ell_p^n$, $p > 0$, into various type of Banach or quasi-Banach spaces. In particular, for $0 <r < p<2$ with $r \le 1$, we construct a family of operators that embed $\ell_p^n$ into $\ell_r^{(1+\eta)n}$, with optimal polynomial bounds in $\eta >0$. Archive classification: math.FA Submitted from: omerfrie(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1107.0992 or http://arXiv.org/abs/1107.0992

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Abstract of a paper by Arseniy Akopyan and Roman Karasev
by alspach＠math.okstate.edu 07 Jul '11

07 Jul '11

This is an announcement for the paper "Kadets type theorems for partitions of a convex body" by Arseniy Akopyan and Roman Karasev. Abstract: For convex partitions of a convex body $B$ we prove that we can put a homothetic copy of $B$ into each set of the partition so that the sum of homothety coefficients is $\ge 1$. In the plane the partition may be arbitrary, while in higher dimensions we need certain restrictions on the partition. Archive classification: math.CO math.FA Mathematics Subject Classification: 52C15, 52C17, 52A40, 52A21 Submitted from: r_n_karasev(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1106.5635 or http://arXiv.org/abs/1106.5635

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Abstract of a paper by J.M.F. Castillo, A. Defant, R. Garcia, D. Perez-Garcia, and J. Suarez
by alspach＠math.okstate.edu 07 Jul '11

07 Jul '11

This is an announcement for the paper "Local complementation and the extension of bilinear mappings" by J.M.F. Castillo, A. Defant, R. Garcia, D. Perez-Garcia, and J. Suarez. Abstract: We study different aspects of the connections between local theory of Banach spaces and the problem of the extension of bilinear forms from subspaces of Banach spaces. Among other results, we prove that if $X$ is not a Hilbert space then one may find a subspace of $X$ for which there is no Aron-Berner extension. We also obtain that the extension of bilinear forms from all the subspaces of a given $X$ forces such $X$ to contain no uniform copies of $\ell_p^n$ for $p\in[1,2)$. In particular, $X$ must have type $2-\varepsilon$ for every $\varepsilon>0$. Also, we show that the bilinear version of the Lindenstrauss-Pe\l czy\'{n}ski and Johnson-Zippin theorems fail. We will then consider the notion of locally $\alpha$-complemented subspace for a reasonable tensor norm $\alpha$, and study the connections between $\alpha$-local complementation and the extendability of $\alpha^*$ -integral operators. Archive classification: math.FA Remarks: to appear in Mathematical Proceedings of the Cambridge Philosophical The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1106.5089 or http://arXiv.org/abs/1106.5089

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Abstract of a paper by Jesus M.F. Castillo, Ricardo Garcia, and Jesus Suarez
by alspach＠math.okstate.edu 07 Jul '11

07 Jul '11

This is an announcement for the paper "Extension and lifting of operators and polynomials" by Jesus M.F. Castillo, Ricardo Garcia, and Jesus Suarez. Abstract: We study the problem of extension and lifting of operators belonging to certain operator ideals, as well as that of their associated polynomials and holomorphic functions. Our results provide a characterization of $\mathcal{L}_1$ and $\mathcal{L}_{\infty}$-spaces that includes and extends those of Lindenstrauss-Rosenthal \cite{LR} using compact operators and Gonz\'{a}lez-Guti\'{e}rrez \cite{GG} using compact polynomials. We display several examples to show the difference between extending and lifting compact (resp. weakly compact, unconditionally convergent, separable and Rosenthal) operators to operators of the same type. Finally, we show the previous results in a homological perspective, which helps the interested reader to understand the motivations and nature of the results presented. Archive classification: math.FA Remarks: to appear in Mediterranean J. of Mathematics Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1106.5088 or http://arXiv.org/abs/1106.5088

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SUMIRFAS 2011
by Bill Johnson 01 Jul '11

01 Jul '11

1st ANNOUNCEMENT OF SUMIRFAS 2011 The Informal Regional Functional Analysis Seminar July 29 - 31 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/conferences/linanalysis/ 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 169. 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 Blocker 148. Speakers at SUMIRFAS 2011 include Gregory Berkolaiko, Nodal count of eigenfunctions and stability of nodal partitions Gilles Godefroy, The complexity of the isomorphism relation on the set of subspaces of a given Banach space: is it possible to improve Gowers' dichotomy? Ciprian Foias, "End of the road" problems in Operator Theory Bill Helton, Free semi-definite programming and its limitations Boris Kashin, N-term approximations and some corrections theorem Constanze Liaw, Dilations and rank one perturbations Eve Oja, The weak metric approximation property of Banach spaces Mihai Putinar, Quillen's phenomenon on pseudoconvex boundaries Jean Roydor, A non-commutative Amir-Cambern Theorem Vladimir Temlyakov, Lebesgue-type inequalities for greedy approximation with respect to redundant systems Steve Dilworth, Daniel Freeman, Denka Kuzarova, Edward Odell (co-chair), and Thomas Schlumprecht (co-chair) are organizing a Concentration Week on "Greedy Algorithms in Banach spaces and Compressed Sensing" for the week of July 18-22. When encoding or reconstructing a vector using an iterative algorithm, a natural approach is to take the best or biggest approximation at each iteration. Such techniques are referred to as greedy algorithms. The theory of compressed sensing is concerned with encoding and reconstructing vectors which are sparsely represented with respect to a given basis. Kevin Ford will present a series of talks on deterministic construction of matrices with the restrictive isometry property. There will be a second series of talks devoted to greedy algorithms and bases. The home page for this Concentration Week is at http://www.math.utexas.edu/users/freeman/greedy11/index.html Florent Baudier (chair), Bill Johnson, Piotr Nowak, and Bunyamin Sari are organizing a Concentration Week on "Non-Linear Geometry of Banach Spaces, Geometric Group Theory, and Differentiability" for the week of August 1-5. The program will include an introductory course by Mark Sapir on coarse embeddings and their applications to geometric group theory, and a series of lectures by Gilles Godefroy on the recent work of the late Nigel Kalton on the coarse classification of Banach spaces. The home page for this Concentration Week is at http://www.math.tamu.edu/~pnowak/index/cw.html We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. When you ask Cara to book your room, please tell her if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. For logistical support, including requests for support, contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, contact William Johnson <johnson(a)math.tamu.edu>, David Larson <larson(a)math.tamu.edu>, Gilles Pisier <pisier(a)math.tamu.edu>, or Joel Zinn <jzinn(a)math.tamu.edu>. For information about the Concentration Week on "Non-Linear Geometry of Banach Spaces, Geometric Group Theory, and Differentiability", contact Florent Baudier <florent(a)math.tamu.edu>. For information about the Concentration Week on "Greedy Algorithms in Banach spaces and Compressed Sensing", contact Edward Odell <odell(a)mail.ma.utexas.edu> or Thomas Schlumprecht <schlump(a)math.tamu.edu>.

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Abstract of a paper by Valentin Ferenczi and Christian Rosendal
by alspach＠math.okstate.edu 27 Jun '11

27 Jun '11

This is an announcement for the paper "On isometry groups and maximal symmetry" by Valentin Ferenczi and Christian Rosendal. Abstract: We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL(X), where X is a separable reﬂexive Banach space. In particular, we provide the ﬁrst known example of a Banach space X without any equivalent maximal norm, or equivalently such that GL(X) contains no maximal bounded subgroup. Moreover, this space X may be chosen to be super-reﬂexive. Archive classification: math.FA math.LO Mathematics Subject Classification: Primary: 22F50, 46B03, 46B04. Secondary: 03E15 Submitted from: rosendal(a)math.uic.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1106.5020 or http://arXiv.org/abs/1106.5020

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Banach