March 2012 - Banach - mathdept.okstate.edu

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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