Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Gianluca Cassese
by alspach＠math.okstate.edu 27 Mar '12

27 Mar '12

This is an announcement for the paper "Some implications of Lebesgue decomposition" by Gianluca Cassese. Abstract: Based on a generalization of Lebesgue decomposition we obtain a characterization of weak compactness in the space $ba$, a representation of its dual space and some results on the structure of finitely additive measures. Archive classification: math.FA Mathematics Subject Classification: Primary 28A25, Secondary 46B50 Submitted from: gianluca.cassese(a)unimib.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1203.1192 or http://arXiv.org/abs/1203.1192

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Abstract of a paper by Antonis Manoussakis and Anna Pelczar-Barwacz
by alspach＠math.okstate.edu 27 Mar '12

27 Mar '12

This is an announcement for the paper "Strictly singular non-compact operators on a class of HI spaces" by Antonis Manoussakis and Anna Pelczar-Barwacz. Abstract: We present a method for constructing bounded strictly singular non-compact operators on mixed Tsirelson spaces defined either by the families (A_n) or (S_n) of a certain class, as well as on spaces built on them, including hereditarily indecomposable spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B15 Remarks: 19 pages Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1203.0243 or http://arXiv.org/abs/1203.0243

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Abstract of a paper by S. A. Argyros, V. Kanellopoulos, and K. Tyros
by alspach＠math.okstate.edu 27 Mar '12

27 Mar '12

This is an announcement for the paper "Higher order spreading models" by S. A. Argyros, V. Kanellopoulos, and K. Tyros. Abstract: We introduce the higher order spreading models associated to a Banach space $X$. Their definition is based on $\ff$-sequences $(x_s)_{s\in\ff}$ with $\ff$ a regular thin family and the plegma families. We show that the higher order spreading models of a Banach space $X$ form an increasing transfinite hierarchy $(\mathcal{SM}_\xi(X))_{\xi<\omega_1}$. Each $\mathcal{SM}_\xi (X)$ contains all spreading models generated by $\ff$-sequences $(x_s)_{s\in\ff}$ with order of $\ff$ equal to $\xi$. We also provide a study of the fundamental properties of the hierarchy. Archive classification: math.FA Mathematics Subject Classification: Primary 46B03, 46B06, 46B25, 46B45, Secondary 05D10 Remarks: 37 pages Submitted from: chcost(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.6390 or http://arXiv.org/abs/1202.6390

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Abstract of a paper by Pawel Wolff
by alspach＠math.okstate.edu 27 Mar '12

27 Mar '12

This is an announcement for the paper "On randomness reduction in the Johnson-Lindenstrauss lemma" by Pawel Wolff. Abstract: A refinement of so-called fast Johnson-Lindenstrauss transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008), is proposed. While it preserves the time efficiency and simplicity of implementation of the original construction, it reduces randomness used to generate the random transformation. In the analysis of the construction two auxiliary results are established which might be of independent interest: a Bernstein-type inequality for a sum of a random sample from a family of independent random variables and a normal approximation result for such a sum. Archive classification: math.PR math.FA Mathematics Subject Classification: 60E15, 46B85 Submitted from: pawel.wolff(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.5500 or http://arXiv.org/abs/1202.5500

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Workshop at A&M
by Bill Johnson 13 Mar '12

13 Mar '12

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2012 The Summer 2012 Workshop in Analysis and Probability at Texas A&M University will be in session from July 2 until August 10, 2012. For information about the Workshop, consult the Workshop Home Page, whose NEW URL is http://www.math.tamu.edu/~kerr/workshop/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 3-5. July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps Between Operator Algebras", organized by Chris Heil, Emily J. King (chair), Keri Kornelson, David Larson (local organizer), and Darrin Speegle. A researcher working in frame theory will naturally be led to consider matrices (the Gram matrix, the analysis operator and the synthesis operator), and many problems in frame theory have a re-casting in operator theory. The most celebrated example of this is the Kadison-Singer problem. By now, there are many mathematicians familiar with the basics of the two areas, and there is a fruitful collaboration. Less obvious is the relationship between frame theory and maps between operator algebras. Very recent work in this area by Han, Larson, Lu, and Lu indicate that this may be a relationship that is ripe for exploiting. The goal of this concentration week is to bring together researchers in these two fields so that they may learn from one another and build networks of potential collaborators. There will be introductory series of talks on "Frame theory" by Ole Christensen, on "Maps on Operator Algebras" by Vern Paulsen, and on "Bridging the Gap Between Frame Theory and Maps on Operator Algebras" by Deguang Han. This concentration week will also lead into a separate conference on the following weekend celebrating the 70th birthday of David Larson. The home page for this Workshop is at http://page.math.tu-berlin.de/~king/cw.html August 6-10 there will be a Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory", organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and Alexei Poltoratski. This CW is designed to bring together two groups of experts: those specializing in complex and harmonic analysis and those working in spectral theory of differential operators and mathematical physics. The main goals of the CW are to study new relationships and to widen further participation in this area in the United States. Introductory series of lectures by Stephen Gustafson, Svetlana Jitomirskaya (to be confirmed), Helge Krueger, and Brett Wick are planned to acquaint non-experts with these topics with the reasonable expectation that some the participants in the larger Workshop will be attracted to this program and inject new ideas into the area. The home page for this Workshop is at http://www.math.tamu.edu/~comech/events/hast-2012/ 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 Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week on "Frame Theory and Maps Between Operator Algebras" contact Emily King <eking(a)math.umd.edu> For information about the Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory" contact Constanze Liaw <conni(a)math.tamu.edu>

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Informal Analysis Seminar at Kent State
by Artem Zvavitch 28 Feb '12

28 Feb '12

Dear Friends, On March 30-April 1, 2012, the Department of Mathematical Science at Kent State University will host famous but still very informal: INFORMAL ANALYSIS SEMINAR and Lecture Series in Ergodic Theory and Probability. The plan for now is to start around 3pm Friday, and finish Sunday Evening (around 5pm). We will have lecture series by Yuval Peres (Microsoft Research) on "Transience of random walks, Unpredictable paths, percolation and Kakeya sets". Mark Rudelson (University of Michigan) on "Invertibility of random matrices". and lectures by Pablo Galindo (Universidad de Valencia / Purdue University), TBA Yun Sung Choi (Postech, Pohang South Korea) on "Slicely countably determined Banach spaces" Miguel Martin (University of Granada) on "The Uniform Convexity, Lushness and Bishop-Phelps-Bollobas Property" Please, also note that on Thursday, March 29 at 4:15pm we will have a Colloquium talk by Sergei Treil (Brown University) at 4:15. More information can be found on http://www.kent.edu/math/events/conferences/informal-analysis-seminar-2012.… The conference fee $65, which includes pick up/drop off from the airport/hotel and Friday/Saturday/Sunday lunches/dinners to be provided at the department. Also, a special price of $135 has been arranged for three nights stay at the Microtel in Streetsboro OH. The reservation must be done through the department. If you plan to stay fewer then 3 nights or prefer to make your own accommodation arrangements please reduce your registration fee by $45 for each day that you will not use our hotel. If possible, please, send a check for your registration fee, made out to "The Department of Mathematical Sciences" to Virginia Wright, The Department of Mathematical Sciences, Kent, State University, Kent, OH, US, 44242. The fee can be also paid during the registration (check/cash). Depending on availability of funds, we may waive the registration fee for young researchers and people without available funding!!!! Please contact Artem Zvavitch (zvavitch(a)math.kent.edu) or Dmitry Ryabogin (ryabogin(a)math.kent.edu) as soon as possible. SORRY FOR THE SHORT NOTICE AND LOOKING FORWARD TO SEEING YOU IN KENT! Very Informal Analysis Group At Kent State

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Abstract of a paper by Cleon S. Barroso
by alspach＠math.okstate.edu 16 Feb '12

16 Feb '12

This is an announcement for the paper "On the minimal space problem and a new result on existence of basic sequences in quasi-Banach spaces" by Cleon S. Barroso. Abstract: We prove that if $X$ is a quasi-normed space which possesses an infinite countable dimensional subspace with a separating dual, then it admits a strictly weaker Hausdorff vector topology. Such a topology is constructed explicitly. As an immediate consequence, we obtain an improvement of a well-known result of Kalton-Shapiro and Drewnowski by showing that a quasi-Banach space contains a basic sequence if and only if it contains an infinite countable dimensional subspace whose dual is separating. We also use this result to highlight a new feature of the minimal quasi-Banach space constructed by Kalton. Namely, which all of its $\aleph_0$-dimensional subspaces fail to have a separating family of continuous linear functionals. Archive classification: math.FA Submitted from: cleonbar(a)mat.ufc.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.3088 or http://arXiv.org/abs/1202.3088

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Abstract of a paper by Sean Li and Assaf Naor
by alspach＠math.okstate.edu 16 Feb '12

16 Feb '12

This is an announcement for the paper "Discretization and affine approximation in high dimensions" by Sean Li and Assaf Naor. Abstract: Lower estimates are obtained for the macroscopic scale of affine approximability of vector-valued Lipschitz functions on finite dimensional normed spaces, completing the work of Bates, Johnson, Lindenstrass, Preiss and Schechtman. This yields a new approach to Bourgain's discretization theorem for superreflexive targets. Archive classification: math.FA math.MG Submitted from: naor(a)cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.2567 or http://arXiv.org/abs/1202.2567

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Abstract of a paper by Kevin Beanland, Daniel Freeman, and Rui Liu
by alspach＠math.okstate.edu 16 Feb '12

16 Feb '12

This is an announcement for the paper "Upper and lower estimates for Schauder frames and atomic decompositions" by Kevin Beanland, Daniel Freeman, and Rui Liu. Abstract: We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable infinite dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking. Archive classification: math.FA Mathematics Subject Classification: 46B20 (Primary), 41A65 (Secondary) Remarks: 22 pages Submitted from: freeman(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.2492 or http://arXiv.org/abs/1202.2492

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Abstract of a paper by Afonso S. Bandeira, Matthew Fickus, Dustin G. Mixon and Percy Wong
by alspach＠math.okstate.edu 16 Feb '12

16 Feb '12

This is an announcement for the paper "The road to deterministic matrices with the restricted isometry property" by Afonso S. Bandeira, Matthew Fickus, Dustin G. Mixon and Percy Wong. Abstract: The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices. Archive classification: math.FA Remarks: 23 pages Submitted from: dmixon(a)princeton.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1202.1234 or http://arXiv.org/abs/1202.1234

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