Banach March 2006

banach@mathdept.okstate.edu

4 participants
8 discussions

Abstract of a paper by Konrad J Swanepoel and Rafael Villa
by Dale Alspach 28 Mar '06

28 Mar '06

This is an announcement for the paper "A lower bound for the equilateral number of normed spaces" by Konrad J Swanepoel and Rafael Villa. Abstract: We show that if the Banach-Mazur distance between an n-dimensional normed space X and ell infinity is at most 3/2, then there exist n+1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an arbitrary n-dimensional normed space admits at least e^{c sqrt(log n)} equidistant points, where c>0 is an absolute constant. We also show that there exist n equidistant points in spaces sufficiently close to n-dimensional ell p (1 < p < infinity). Archive classification: Metric Geometry; Functional Analysis Mathematics Subject Classification: 46B04 (Primary); 46B20, 52A21, 52C17 (Secondary) Remarks: 5 pages The source file(s), equilateral-lower3.tex: 14633 bytes, is(are) stored in gzipped form as 0603614.gz with size 5kb. The corresponding postcript file has gzipped size 39kb. Submitted from: swanekj(a)unisa.ac.za The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0603614 or http://arXiv.org/abs/math.MG/0603614 or by email in unzipped form by transmitting an empty message with subject line uget 0603614 or in gzipped form by using subject line get 0603614 to: math(a)arXiv.org.

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Workshop at A&M
by Bill Johnson 23 Mar '06

23 Mar '06

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2006 The Summer 2006 session of the Workshop in Linear Analysis and Probability at Texas A&M University will be in session from July 10 until August 11. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 4-6. Sanjeev Aurora <arora(a)CS.Princeton.EDU>, Moses Charikar <moses(a)CS.Princeton.EDU>, Bill Johnson <johnson(a)math.tamu.edu>, Nati Linial <nati(a)cs.huji.ac.il>, and Assaf Naor <anaor(a)microsoft.com> are organizing a Concentration Week on "Metric Geometry and Geometric Embeddings of Discrete Metric Spaces" that will take place July 17-22. The purpose of the Concentration Week is to bring together researchers in Computer Science, Analysis, and Geometric Group Theory who are interested in various aspects of metric geometry in the expectation that interaction among experts, students, and post docs in the various areas will be fruitful. The first day will be devoted to introductory talks designed to introduce non experts to the subject. Pete Casazza <pete(a)math.missouri.edu>, David Larson <larson(a)math.tamu.edu>, Gestur Olafsson <olafsson(a)math.lsu.edu>, and Thomas Schlumprecht <schlump(a)math.tamu.edu> are organizing a Concentration Week on "Frames, Banach spaces and Signal Processing" that will take place August 7 - August 11. The purpose of the Concentration Week is to bring researchers in Frame and Wavelet theory / Signal and Image processing together with researchers in Banach space theory to generate a "cross-fertilization" of areas. 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(a)math.tamu.edu>. For more information on the Workshop itself, please 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 "Metric Geometry and Geometric Embeddings of Discrete Metric Spaces", contact Bill Johnson <johnson(a)math.tamu.edu>. For information about the Concentration Week on "Frames, Banach spaces and Signal Processing" contact David Larson <larson(a)math.tamu.edu> or Thomas Schlumprecht <schlump(a)math.tamu.edu>.

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Abstract of a paper by Emanuel Milman
by Dale Alspach 21 Mar '06

21 Mar '06

This is an announcement for the paper "A remark on two duality relations" by Emanuel Milman. Abstract: We remark that an easy combination of two known results yields a positive answer, up to log(n) terms, to a duality conjecture that goes back to Pietsch. In particular, we show that for any two symmetric convex bodies K,T in R^n, denoting by N(K,T) the minimal number of translates of T needed to cover K, one has: N(K,T) <= N(T*,(C log(n))^{-1} K*)^{C log(n) loglog(n)}, where K*,T* are the polar bodies to K,T, respectively, and C > 1 is a universal constant. As a corollary, we observe a new duality result (up to log(n) terms) for Talagrand's \gamma_p functionals. Archive classification: Functional Analysis; Metric Geometry Remarks: 13 pages The source file(s), Duality-Of-Entropy.bbl: 4703 bytes, Duality-Of-Entropy.tex: 31314 bytes, is(are) stored in gzipped form as 0603461.tar.gz with size 12kb. The corresponding postcript file has gzipped size 60kb. Submitted from: emanuel.milman(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0603461 or http://arXiv.org/abs/math.FA/0603461 or by email in unzipped form by transmitting an empty message with subject line uget 0603461 or in gzipped form by using subject line get 0603461 to: math(a)arXiv.org.

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Abstract of a paper by Stanislaw J. Szarek
by Dale Alspach 15 Mar '06

15 Mar '06

This is an announcement for the paper "Still more on norms of completely positive maps" by Stanislaw J. Szarek. Abstract: King and Ruskai asked whether the norm of a completely positive map acting between Schatten classes of operators is equal to that of its restriction to the real subspace of self-adjoint operators. Proofs have been promptly supplied by Watrous and Audenaert. Here we provide one more proof, in fact of a slightly more general fact, under the (slightly weaker) assumption of 2-positivity. The argument is elementary and self-contained. Archive classification: Quantum Physics; Functional Analysis Remarks: 2 pages Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/quant-ph/0603110 or http://arXiv.org/abs/quant-ph/0603110 or by email in unzipped form by transmitting an empty message with subject line uget /0603110 or in gzipped form by using subject line get /0603110 to: math(a)arXiv.org.

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LMS meeting and workshop in functional analysis
by J R Partington 15 Mar '06

15 Mar '06

LMS Northern Regional Meeting and Workshop in Functional Analysis There will be a Meeting of the London Mathematical Society at the University of Leeds, UK on Monday 3rd July 2006, at which the speakers will be: Uffe Haagerup (Odense) and Nigel Kalton (Missouri). This is to be followed by a workshop on functional analysis, the theme being "bounded and unbounded operators on Banach and Hilbert spaces". Haagerup and Kalton will give further talks, and additional speakers include: Michel Crouzeix (Rennes), Ken Davidson (Waterloo), Alexander Helemskii (Moscow), Thomas Ransford (Laval and Oxford), Thomas Schlumprecht (Texas A&M), Hanne Schultz (Odense), Steen Thorbjoernsen (Odense), and Lutz Weis (Karlsruhe). For full details and instructions how to register for the meeting, see http://www.maths.leeds.ac.uk/pure/analysis/lms/ Jonathan R. Partington j.r.partington(a)leeds.ac.uk

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Abstract of a paper by Valentin Ferenczi
by Dale Alspach 09 Mar '06

09 Mar '06

This is an announcement for the paper "A Banach space dichotomy for quotients of subspaces" by Valentin Ferenczi. Abstract: A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. A reflexive space with the restricted QHI property is in particular HI, has HI dual, and is saturated with subspaces which are HI and have HI dual. The following dichotomy theorem is proved: any infinite dimensional Banach space contains a quotient of subspace which either has an unconditional basis, or has the restricted QHI property. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03, 46B10 Remarks: 25 pages The source file(s), dichotomyferenczi0306.tex: 67293 bytes, is(are) stored in gzipped form as 0603188.gz with size 20kb. The corresponding postcript file has gzipped size 78kb. Submitted from: ferenczi(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0603188 or http://arXiv.org/abs/math.FA/0603188 or by email in unzipped form by transmitting an empty message with subject line uget 0603188 or in gzipped form by using subject line get 0603188 to: math(a)arXiv.org.

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Abstract of a paper by E. Odell, Th. Schlumprecht, and A. Zsak
by Dale Alspach 07 Mar '06

07 Mar '06

This is an announcement for the paper "On the structure of asymptotic l_p spaces" by E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic l_p FDD. More general results of this type are also obtained. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20 Remarks: 32 pages The source file(s), asymptotic-ell-p.tex: 108321 bytes, is(are) stored in gzipped form as 0603063.gz with size 30kb. The corresponding postcript file has gzipped size 143kb. Submitted from: a.zsak(a)dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0603063 or http://arXiv.org/abs/math.FA/0603063 or by email in unzipped form by transmitting an empty message with subject line uget 0603063 or in gzipped form by using subject line get 0603063 to: math(a)arXiv.org.

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Conference on Banach space theory
by Félix Cabello Sánchez 02 Mar '06

02 Mar '06

Banach space theory: classical topics and new directions 4-8 September 2006 · Cáceres · Spain http://www.banachspaces.com A Satellite Conference of the International Congress of Mathematicians, Madrid 2006 The conference aims to contemplate the topic of Banach spaces from an open and broader point of view; so, in addition to classical Banach space theory, related topics of active research have been included. The main lines of the conference are: · Structure and geometry of infinite dimensional Banach and quasi-Banach spaces. · Infinite dimensional topology. · Asymptotic geometric analysis. · Categorical and homological methods. · Applications of descriptive set theory. PROGRAM During the mornings there will take place the invited lectures MAIN SPEAKERS S. Argyros, National Technical University, Athens, Greece. K. Ball, University College London, London, UK. J. Bastero, Universidad de Zaragoza, Zaragoza, Spain. F. Bombal, Universidad Complutense, Madrid, Spain. G. Godefroy, Université Paris 6, Paris, France. N.J. Kalton, University of Missouri, Columbia (Missouri), USA. V. Milman, University of Tel Aviv, Tel Aviv, Israel. A. Naor, Microsoft Research, Redmond (Washington), USA. J. Orihuela, Universidad de Murcia, Murcia, Spain. A. Rodríguez-Palacios, Universidad de Granada, Granada, Spain. S. Szarek, Case Western Reserve University, Cleveland (Ohio), USA. E. Odell, University of Texas, Austin (Texas), USA. M. Valdivia, Universidad de Valencia, Valencia, Spain. SCIENTIFIC COMMITTEE J.M.F. Castillo, Universidad de Extremadura, Badajoz, Spain (Coordinator). W.B. Johnson, Texas A&M University, U.S.A. J. Lindenstrauss, Hebrew University, Jerusalem, Israel. B. Maurey, Université Paris 7, France. A. Pajor, Université de Marne-la-Vallée, France. A. Pelczynski, Polish Academy of Sciences, Warsawa, Poland. D. Preiss, University College, London, England. N. Tomczak-Jaegermann, University of Alberta, Canada. CONTRIBUTED TALKS During the evenings there will be sessions of contributed talks of 15-30 min. People willing to deliver a talk are kindly encouraged to send a message to the organization (banach(a)unex.es) or visit the web site of the conference (http://www.banachspaces.com) and click the icon contributed talks. The deadline for submission of abstracts is 31 May 2006. THEMATIC SESSIONS There is the possibility to group contributed talks in thematic sessions. People interested in organizing such sessions please send a proposal to the coordinator (castillo(a)unex.es). PLACE The conference will take place in Cáceres, in the Complejo Cultural S. Francisco. The old town of Cáceres has been declared by the Unesco part of the World Heritage (at the home-page of the conference there is a link to perform a virtual tour). Cáceres is well connected with Madrid by either bus or train. The Complejo S. Francisco is an old palace of XIV siecle entirely reformed and kindly leased by the Diputación de Cáceres for this meeting. Information and pictures of the palace can be seen at the home-page of the conference. REGISTRATION. There will be a registration fee of 100 EURO (150 EURO after 15 May 2006), with a reduced fee of 50 EURO for students. Click the icon registration at http://www.banachspaces.com to see the different possibilities of payment. ACCOMMODATION. There is the possibility of housing at the Residence Diego Muñoz Torrero, placed in front of the Complejo S. Francisco, site of the conference. The price of is 30 EURO per day and person in a double room. There is also a combined offer registration fee + accommodation at the Residence + breakfast + lunch (not dinner) during all the Conference for a total of 300 EURO. CONTACT Departamento de Matemáticas, Universidad de Extremadura, Avda de Elvas s/n, 06071-Badajoz Spain Phone: +34 924 289 563 Fax: +34 924 272 911 e-mail: banach(a)unex.es ORGANIZATION Javier Alonso, Patricia Arjona, Francisco Arranz, Manolo Báez, Carlos Benítez, Félix Cabello Sánchez, Carmen Calvo, Jesús M.F. Castillo, Rosa Díez, Manuel Fernández García-Hierro, Juan Antonio García, Ricardo García, Germán Giraldez, Eva López, Pedro Martín, Francisco Montalvo, Yolanda Moreno, Mª Angeles Mulero, Antonio Oyola, Carmen Ortiz, Paloma Pérez, Antonio Pulgarín, Mª Luisa Soriano, Jesús Suárez, Antonio Ullán, Diego Yáñez. PREVIOUS CONFERENCES Since 1996, the Department of Mathematics of the University of Extremadura organizes the even years a Banach space conference in either Badajoz or Cáceres. The proceedings of Conferences I-IV have appeared in Extracta Mathematicae, and can be found in the journal web-site http://unex.es/extracta/extracta.html. The proceedings of the V Conference will be published by the Cambridge University Press as a volume in the Lecture Notes Series of the London Mathematical Society. All information about the V Conference (Cáceres 2004) and its proceedings can be found at the web-site http://www.banachspaces.com/banach04/ -- Banach space theory: classical topics & new directions Caceres, 4-8 September 2006

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Banach March 2006