Banach September 2010

banach@mathdept.okstate.edu

5 participants
20 discussions

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu), so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Sonia Berrios and Geraldo Botelho
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Approximation properties determined by operator ideals" by Sonia Berrios and Geraldo Botelho. Abstract: Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in projective tensor products, spaces of linear functionals, spaces of homogeneous polynomials (in particular, spaces of linear operators), spaces of holomorphic functions and their preduals. Archive classification: math.FA Remarks: 24 pages Submitted from: botelho(a)ufu.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2977 or http://arXiv.org/abs/1009.2977

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Abstract of a paper by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Dichotomy theorems for random matrices and closed ideals of operators on $\big(\bigoplus _{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$" by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak. Abstract: We prove two dichotomy theorems about sequences of operators into $L_1$ given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on $\ell_1^k$ $(k\in\mathbb N$) or uniformly approximately factor through $\mathrm{c}_0$. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the space $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$. Archive classification: math.FA Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20, 46B45 (secondary) Remarks: 22 pages Submitted from: andras.zsak(a)maths.nottingham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2923 or http://arXiv.org/abs/1009.2923

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Abstract of a paper by Daniel Pellegrino
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "A note on the best constants for the Bohnenblust-Hille inequality" by Daniel Pellegrino. Abstract: In this note we show that a recent new proof of Bohnenblust-Hille inequality, due to Defant et al, combined with the better known constant for Littlewood 4/3 theorem and the optimal constants of Khinchin inequality, due to Haagerup, provide quite better estimates for the constants involved in the Bohnenblust-Hille inequality. For example, if $2\leq m\leq13,$ we show that the constants $C_{m}=2^{(m-1)/2}$ can be replaced by $2^{\frac{m^{2}+m-6}{4m}% }K_{G}^{2/m}$, which are substantially better than $C_{m}$ (here $K_{G}$ denotes the complex Grothendieck Archive classification: math.FA Remarks: 7 pages Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2717 or http://arXiv.org/abs/1009.2717

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Abstract of a paper by Stanislav Shkarin
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "A complete locally convex space of countable dimension admitting an operator with no invariant subspaces" by Stanislav Shkarin. Abstract: We construct a complete locally convex topological vector space $X$ of countable algebraic dimension and a continuous linear operator $T:X\to X$ such that $T$ has no non-trivial closed invariant subspaces. Archive classification: math.FA Mathematics Subject Classification: 47A16 Submitted from: s.shkarin(a)qub.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2644 or http://arXiv.org/abs/1009.2644

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Abstract of a paper by Elias Pipping
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "L- and M-structure in lush spaces" by Elias Pipping. Abstract: Let $X$ be a Banach space which is lush. It is shown that if a subspace of $X$ is either an L-summand or an M-ideal then it is also lush. Archive classification: math.FA Submitted from: pipping(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2232 or http://arXiv.org/abs/1009.2232

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Abstract of a paper by Thierry Gallay and Denis Serre
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "The numerical measure of a complex matrix" by Thierry Gallay and Denis Serre. Abstract: We introduce and carefully study a natural probability measure over the numerical range of a complex matrix $A \in M_n(\C)$. This numerical measure $\mu_A$ can be defined as the law of the random variable $<AX,X> \in \C$ when the vector $X \in \C^n$ is uniformly distributed on the unit sphere. If the matrix $A$ is normal, we show that $\mu_A$ has a piecewise polynomial density $f_A$, which can be identified with a multivariate $B$-spline. In the general (nonnormal) case, we relate the Radon transform of $\mu_A$ to the spectrum of a family of Hermitian matrices, and we deduce an explicit representation formula for the numerical density which is appropriate for theoretical and computational purposes. As an application, we show that the density $f_A$ is polynomial in some regions of the complex plane which can be characterized geometrically, and we recover some known results about lacunas of symmetric hyperbolic systems in $2+1$ dimensions. Finally, we prove under general assumptions that the numerical measure of a matrix $A \in M_n(\C)$ concentrates to a Dirac mass as the size $n$ goes to infinity. Archive classification: math.FA math.PR math.SP Mathematics Subject Classification: 47A12, 28A33, 44A12, 65D07, 35L40, 60F05 Remarks: 41 pages, 5 figures Submitted from: thierry.gallay(a)ujf-grenoble.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.1522 or http://arXiv.org/abs/1009.1522

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Abstract of a paper by Jan Vybiral
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Average best $m$-term approximation" by Jan Vybiral. Abstract: We introduce the concept of average best $m$-term approximation widths with respect to a probability measure on the unit ball of $\ell_p^n$. We estimate these quantities for the embedding $id:\ell_p^n\to\ell_q^n$ with $0<p\le q\le \infty$ for the normalized cone and surface measure. Furthermore, we consider certain tensor product weights and show that a typical vector with respect to such a measure exhibits a strong compressible (i.e. nearly sparse) structure. Archive classification: math.FA math.NA math.ST stat.TH Mathematics Subject Classification: 41A46 (Primary) 46B20, 60B11 (Secondary) Remarks: 2 figures Submitted from: jan.vybiral(a)oeaw.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.1751 or http://arXiv.org/abs/1009.1751

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Abstract of a paper by Daniel Carando, Veronica Dimant, and Santiago Muro
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Every Banach ideal of polynomials is compatible with an operator ideal" by Daniel Carando, Veronica Dimant, and Santiago Muro. Abstract: We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of $n$-homogeneous polynomials belongs to a coherent sequence of ideals of $k$-homogeneous polynomials. Archive classification: math.FA Mathematics Subject Classification: 47H60, 47L20, 47L22 (Primary) 46G25 (Secondary) Remarks: 12 pages Submitted from: smuro(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.1064 or http://arXiv.org/abs/1009.1064

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Abstract of a paper by Gideon Schechtman
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$" by Gideon Schechtman. Abstract: Using a recent result of Batson, Spielman and Srivastava, We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even integer, needed to almost isometrically contain all $k$-dimensional subspaces of $L_p$. Archive classification: math.FA Submitted from: gideon(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.1061 or http://arXiv.org/abs/1009.1061

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Banach September 2010