November 2011 - Banach - mathdept.okstate.edu

Abstract of a paper by Jakub Olejnik
by alspach＠math.okstate.edu 01 Nov '11

01 Nov '11

This is an announcement for the paper "On a complete characterization of a.s.\ convergence of multiple orthogonal series" by Jakub Olejnik. Abstract: We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences $(a_{n_1\ldots n_d})_{n_1,\ldots,n_d\in\bb N}$ such that for all orthonormal $(\Phi_{n_1\ldots n_d})$ multiple orthogonal series $\sum_{n_1,\ldots,n_d\in\bb N}a_{n_1\ldots n_d}\Phi_{n_1\ldots n_d}$ are a.s.\ convergent. Archive classification: math.FA math.PR Mathematics Subject Classification: 60G60, 60G17 (MSC2010) Submitted from: jakubo(a)math.uni.lodz.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.3942 or http://arXiv.org/abs/1110.3942

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Abstract of a paper by Daniel Galicer, Silvia Lassalle and Pablo Turco
by alspach＠math.okstate.edu 01 Nov '11

01 Nov '11

This is an announcement for the paper "The ideal of p-compact operators: a tensor product approach" by Daniel Galicer, Silvia Lassalle and Pablo Turco. Abstract: We study the space of $p$-compact operators $\mathcal K_p$, using the theory of tensor norms and operator ideals. We prove that $\mathcal K_p$ is associated to $/d_p$, the left injective associate of the Chevet-Saphar tensor norm $d_p$ (which is equal to $g_{p'}'$). This allows us to relate the theory of $p$-summing operators with that of $p$-compact operators. With the results known for the former class and appropriate hypothesis on $E$ and $F$ we prove that $\mathcal K_p(E;F)$ is equal to $\mathcal K_q(E;F)$ for a wide range of values of $p$ and $q$, and show that our results are sharp. We also exhibit several structural properties of $\mathcal K_p$. For instance, we obtain that $\mathcal K_p$ is regular, surjective, totally accessible and characterize its maximal hull $\mathcal K_p^{max}$ as the dual ideal of the $p$-summing operators, $\Pi_p^{dual}$. Furthermore, we prove that $\mathcal K_p$ coincides isometrically with $\mathcal {QN}_p^{dual}$, the dual ideal of the quasi $p$-nuclear operators. Archive classification: math.FA Mathematics Subject Classification: 47L20, 46A32, 47B07, 47B10 Remarks: 18 pages Submitted from: paturco(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.3251 or http://arXiv.org/abs/1110.3251

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Abstract of a paper by Valentin Ferenczi and Christian Rosendal
by alspach＠math.okstate.edu 01 Nov '11

01 Nov '11

This is an announcement for the paper "Displaying Polish groups on separable Banach spaces" by Valentin Ferenczi and Christian Rosendal. Abstract: A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology. Displays of Polish groups on separable real spaces are studied. It is proved that any closed subgroup of the infinite symmetric group S_\infty containing a non-trivial central involution admits a display on any of the classical spaces c0, C([0,1]), lp and Lp for 1 <=p <\infty. Also, for any Polsih group G, there exists a separable space X on which {-1,1} x G has a display. Archive classification: math.GR math.FA math.LO Mathematics Subject Classification: 20E08, 03E15, 46B03 Remarks: 27 pages Submitted from: ferenczi(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.2970 or http://arXiv.org/abs/1110.2970

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