April 2013 - Banach - mathdept.okstate.edu

Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
by alspach＠math.okstate.edu 12 Apr '13

12 Apr '13

This is an announcement for the paper "Mean width of random perturbations of random polytopes" by David Alonso-Gutierrez and Joscha Prochno. Abstract: We prove some "high probability" results on the expected value of the mean width for random perturbations of random polytopes. The random perturbations are considered for Gaussian and $p$-stable random vectors, as well as uniform distributions on $\ell_p^N$-balls and the unit sphere. Archive classification: math.FA math.PR Mathematics Subject Classification: Primary 52A22, Secondary 52A23, 05D40 Submitted from: joscha.prochno(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.5677 or http://arXiv.org/abs/1303.5677

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Abstract of a paper by P. Wojtaszczyk
by alspach＠math.okstate.edu 12 Apr '13

12 Apr '13

This is an announcement for the paper "On left democracy function" by P. Wojtaszczyk. Abstract: We continue the study undertaken in \cite{GHN} of left democracy function $h_l(N)=\inf_{\#\Lambda=N}\left\|\sum_{n\in \Lambda_N} x_n\right\| $ of an unconditional basis in a Banach space $X$. We provide an example of a basis with $h_l$ non-doubling. Then we show that for bases with non-doubling $h_l$ the greedy projection is not optimal. Together with results from \cite{GHN} and improved by C. Cabrelli, G. Garrig\'os, E. Hernandez and U. Molter we get that the basis is greedy if and only if the greedy projection is optimal. Archive classification: math.FA Submitted from: wojtaszczyk(a)mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.4972 or http://arXiv.org/abs/1303.4972

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Abstract of a paper by Daniel Beltita, Sasmita Patnaik, and Gary Weiss
by alspach＠math.okstate.edu 12 Apr '13

12 Apr '13

This is an announcement for the paper "$B(H)$-Commutators: A historical survey II and recent advances on commutators of compact operators" by Daniel Beltita, Sasmita Patnaik, and Gary Weiss. Abstract: A sequel to \cite{gW05}, we address again the single commutator problem \cite{PT71} of Pearcy and Topping: Is every compact operator a single commutator of compact operators? by focusing on a 35 year old test question for this posed in 1976 by the last named author and others: Are there any strictly positive operators that are single commutators of compact operators? The latter we settle here affirmatively with a modest modification of Anderson's fundamental construction \cite{jA77} constructing compact operators whose commutator is a rank one projection. Moreover we provide here a rich class of such strictly positive operators that are commutators of compact operators and pose a question for the rest. We explain also how these methods are related to the study of staircase matrix forms, their equivalent block tri-diagonal forms, and commutator problems. In particular, we present the original test question and solution that led to the negative solution of the Pearcy-Topping question on whether or not every trace class trace zero operator was a commutator (or linear combination of commutators) of Hilbert-Schmidt operators. And we show how this evolved from staircase form considerations along with a Larry Brown result on trace connections to ideals \cite{lB94} which itself is at the core of \cite[Section 7]{DFWW}. The omission in \cite{gW05} of this important 35 year old test question was inadvertent and we correct that in this paper. This sequel starts where [ibid] left off but can be read independently of [ibid]. The present paper also has a section on self-commutator equations $[X^*,X]=A$ within the framework of some classical operator Lie algebras. That problem was solved by Fan and Fong (1980) for the full algebra of compact operators, and we solve it here for the complex symplectic Lie algebra of compact operators and for complex semisimple Lie algebras. Archive classification: math.OA math.FA math.RT Mathematics Subject Classification: Primary: 47B47, 47B10, 47L20, Secondary: 47-02, 47L30, 17B65, Remarks: 20 pages Submitted from: Daniel.Beltita(a)imar.ro The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.4844 or http://arXiv.org/abs/1303.4844

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Workshop at A&M
by Bill Johnson 11 Apr '13

11 Apr '13

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2013 The Summer 2013 Workshop in Analysis and Probability at Texas A&M University will be in session from July 15 until August 16, 2013. For information about the Workshop, consult the Workshop Home Page, whose URL is http://www.math.tamu.edu/~kerr/workshop/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 2-4. SUMIRFAS will be dedicated to the memory of Ted Odell, who was one of the organizers of the UTAMIRFAS, the predecessor of SUMIRFAS. Ted served on the advisory board of the Workshop since its beginning. Plenary speakers at SUMIRFAS include Stephen Dilworth, Steve Jackson, Masoud Khalkhali, Thomas Schlumprecht, Nicole Tomczak-Jaegermann, and Wilhelm Winter. August 5-9 there will be a Concentration Week on "Dynamics, Geometry, and Operator Algebras", organized by David Kerr and Guoliang Yu. This Concentration Week aims to promote connections between nuclearity, nuclear dimension, group C*-algebras and crossed products, topological and measurable dynamics, algebraic dynamics, entropy, dimensional ideas from coarse geometry, and K-theory with applications to topology. The program will feature lecture series by David Kerr, Stuart White, and Rufus Willett. The URL for this Concentration Week is http://www.math.tamu.edu/~kerr/concweek13/ Immediately preceding SUMIRFAS, on August 1, there will be a celebration of "The Mathematical Legacy of Ted Odell", organized by Thomas Schlumprecht. 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 "Dynamics, Geometry, and Operator Algebras" contact David Kerr <kerr(a)math.tamu.edu>. For information about the day devoted to "The Mathematical Legacy of Ted Odell" contact Thomas Schlumprecht <schlump(a)math.tamu.edu>

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