Banach

banach@mathdept.okstate.edu

2549 discussions

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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Abstract of a paper by V.L. Dolnikov and R.N. Karasev
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Dvoretzky type theorems for multivariate polynomials and sections of convex bodies" by V.L. Dolnikov and R.N. Karasev. Abstract: In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. The latter conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture. Archive classification: math.MG math.AT math.CO math.FA Mathematics Subject Classification: 46B20, 05D10, 26C10, 52A21, 52A23, 55M35 Submitted from: r_n_karasev(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.0392 or http://arXiv.org/abs/1009.0392

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Meeting: Integration, Vector Measures and Related Topics IV'' Dedicated to Joe Diestel. Murcia 2011
by IntMedVec Murcia 2011 17 Sep '10

17 Sep '10

Meeting: Integration, Vector Measures and Related Topics IV'' Dedicated to Joe Diestel. University of Murcia, Murcia, Spain March 2 - March 5, 2011 Description: The aim of this four day conference is to bring together experienced and novice researchers interested in Integration, Vector Measures and their Applications. The conference will feature a series of plenary and short lectures as well as a mini-course and contributed posters on recent advances in the subject. The previous meetings of this series of conferences were held in Valencia in 2004, Sevilla in 2006 and Eichstätt in 2008. Partial support for a small number of participants is expected to be available. Recent recipients of doctoral degrees and pre-doc students are encouraged to apply. The meeting will take place in La Manga del Mar Menor, Murcia, from March 2? March 5, 2011 (both days included). It will be organized by the Functional Analysis Group of the University of Murcia. Information: http://www.um.es/beca/Murcia2011/index.php Sponsors: UMU, MCIN, iMath Consolider, Fundacion Seneca CARM On behalf of the organizers. Integration, Vector Measures and Related Topics IV. Murcia. March 2-5. 2011 http://www.um.es/beca/Murcia2011/index.php

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Abstract of a paper by Mohammad Sal Moslehian and John M. Rassias
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "A characterization of inner product spaces" by Mohammad Sal Moslehian and John M. Rassias. Abstract: In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \|\cdot\|)$ is an inner product space if $$\sum_{\varepsilon_i \in \{-1,1\}} \left\|x_1 + \sum_{i=2}^k\varepsilon_ix_i\right\|^2=\sum_{\varepsilon_i \in \{-1,1\}} \left(\|x_1\| + \sum_{i=2}^k\varepsilon_i\|x_i\|\right)^2\,,$$ for some positive integer $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Conversely, if $(X, \|\cdot\|)$ is an inner product space, then the equality above holds for all $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Archive classification: math.FA math.CA Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05 Remarks: 8 Pages, to appear in Kochi J. Math. (Japan) Submitted from: moslehian(a)ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.0079 or http://arXiv.org/abs/1009.0079

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Abstract of a paper by Iosif Pinelis
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "On the von Bahr--Esseen inequality" by Iosif Pinelis. Abstract: The well-known von Bahr--Esseen bound on the absolute pth moments of martingales with p in (1,2] is extended to a large class of moment functions, and now with a best possible constant factor (which depends on the moment function). As an application, measure concentration inequalities for separately Lipschitz functions on product spaces are obtained. Relations with p-uniformly smooth and q-uniformly convex normed spaces are discussed. Archive classification: math.PR math.FA Mathematics Subject Classification: Primary 60E15, 60B11, 62G10, secondary 46B09, 46B20, 46B10 Submitted from: ipinelis(a)mtu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.5350 or http://arXiv.org/abs/1008.5350

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