Banach October 2009

banach@mathdept.okstate.edu

1 participants
18 discussions

Abstract of a paper by T. Bosenko and V. Kadets
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "Daugavet centers" by T. Bosenko and V. Kadets. Abstract: An operator $G {:}\allowbreak\ X \to Y$ is said to be a Daugavet center if $\|G + T\| = \|G\| + \|T\|$ for every rank-$1$ operator $T {:}\allowbreak\ X \to Y$. The main result of the paper is: if $G {:}\allowbreak\ X \to Y$ is a Daugavet center, $Y$ is a subspace of a Banach space \, $E$, and $J: Y \to E$ is the natural embedding operator, then $E$ can be equivalently renormed in such a way, that $J \circ G : X \to E$ is also a Daugavet center. This result was previously known for particular case $X=Y$, $G=\mathrm{Id}$ and only in separable spaces. The proof of our generalization is based on an idea completely different from the original one. We give also some geometric characterizations of Daugavet centers, present a number of examples, and generalize (mostly in straightforward manner) to Daugavet centers some results known previously for spaces with the Daugavet property. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B03, 46B25, 47B38 The source file(s), bosenko-kadets-Daugavet-centers.tex: 50780 bytes, is(are) stored in gzipped form as 0910.4503.gz with size 14kb. The corresponding postcript file has gzipped size 109kb. Submitted from: t.bosenko(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.4503 or http://arXiv.org/abs/0910.4503 or by email in unzipped form by transmitting an empty message with subject line uget 0910.4503 or in gzipped form by using subject line get 0910.4503 to: math(a)arXiv.org.

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Abstract of a paper by Spiros A. Argyros, Kevin Beanland, and Theocharis Raikoftsalis
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "A weak Hilbert space with few symmetries" by Spiros A. Argyros, Kevin Beanland, and Theocharis Raikoftsalis. Abstract: We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on Y is of the form D+S where S is a strictly singular operator and D is a diagonal operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces. Archive classification: math.FA Remarks: 32 pages The source file(s), WeakHilbert.tex: 88673 bytes, is(are) stored in gzipped form as 0910.4401.gz with size 26kb. The corresponding postcript file has gzipped size 157kb. Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.4401 or http://arXiv.org/abs/0910.4401 or by email in unzipped form by transmitting an empty message with subject line uget 0910.4401 or in gzipped form by using subject line get 0910.4401 to: math(a)arXiv.org.

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Abstract of a paper by Kevin Beanland and Frank Sanacory
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "Spreading models in the duals of Schlumprecht-type spaces" by Kevin Beanland and Frank Sanacory. Abstract: We show that the dual of Schlumprecht's space $S^*$ and the dual of Gowers and Maurey's HI space each contain a $c_0$ spreading model and that for each $1 < p < \infty$ and $1/p+1/q=1$, the dual of the $p$-convexification of Schlumprecht's space and the dual of its HI counterpart, constructed by Neil Dew, each contain an $\ell_q$ spreading model. The existence of a $c_0$ spreading model in $S^*$ solves a problem of S. A. Argyros. We also give a general criteria for the existence of a bounded non-compact operator and use this to show that there exist strictly singular non-compact operators on each of these spaces. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 14 pages The source file(s), CoinSstarfinal.bbl: 3840 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.4400 or http://arXiv.org/abs/0910.4400 or by email in unzipped form by transmitting an empty message with subject line uget 0910.4400 or in gzipped form by using subject line get 0910.4400 to: math(a)arXiv.org.

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Abstract of a paper by Daniel Carando and Daniel Galicer
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "Extending polynomials in maximal and minimal ideals" by Daniel Carando and Daniel Galicer. Abstract: Given an homogeneous polynomial on a Banach space $E$ belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of $E$ and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron-Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allow us to obtain symmetric versions of some basic results of the metric theory of tensor products. Archive classification: math.FA Mathematics Subject Classification: 46G25; 46A32; 46B28; 47H60 Remarks: 10 pages The source file(s), ExtendingCarandoGalicer.tex: 34351 bytes, is(are) stored in gzipped form as 0910.3888.gz with size 11kb. The corresponding postcript file has gzipped size 93kb. Submitted from: dgalicer(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3888 or http://arXiv.org/abs/0910.3888 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3888 or in gzipped form by using subject line get 0910.3888 to: math(a)arXiv.org.

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Abstract of a paper by S. J. Dilworth, D. Freeman, E. Odell and Th. Schlumprecht
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "Greedy bases for Besov spaces" by S. J. Dilworth, D. Freeman, E. Odell and Th. Schlumprecht. Abstract: We prove thatthe Banach space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which is isomorphic to certain Besov spaces, has a greedy basis whenever $1\leq p \leq\infty$ and $1<q<\infty$. Furthermore, the Banach spaces $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_1}$, with $1<p\le \infty$, and $(\oplus_{n=1}^\infty \ell_p^n)_{c_0}$, with $1\le p<\infty$ do not have a greedy bases. We prove as well that the space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$ has a 1-greedy basis if and only if $1\leq p=q\le \infty$. Archive classification: math.FA Mathematics Subject Classification: 46B15, 41A65 The source file(s), dfos_greedy_101609.tex: 45739 bytes, is(are) stored in gzipped form as 0910.3867.gz with size 14kb. The corresponding postcript file has gzipped size 110kb. Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3867 or http://arXiv.org/abs/0910.3867 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3867 or in gzipped form by using subject line get 0910.3867 to: math(a)arXiv.org.

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Abstract of a paper by Jakub Onufry Wojtaszczyk
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "No return to convexity" by Jakub Onufry Wojtaszczyk. Abstract: In the paper we study closures of classes of log--concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class $\mathcal{K}$. In particular we prove that if one starts from one--dimensional log--concave measures, one obtains no non--trivial uniform mesures on convex bodies. The operations we consider are easily proved to preserve a number of important properties, including a uniform bound on the isotropic constant and $IC$ inequalities. Archive classification: math.FA math.MG math.PR Mathematics Subject Classification: 52A23 Remarks: 12 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: onufryw(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3288 or http://arXiv.org/abs/0910.3288 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3288 or in gzipped form by using subject line get 0910.3288 to: math(a)arXiv.org.

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Abstract of a paper by Guillaume Aubrun, Stanislaw Szarek, and Elisabeth Werner
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "Non-additivity of Renyi entropy and Dvoretzky's Theorem" by Guillaume Aubrun, Stanislaw Szarek, and Elisabeth Werner. Abstract: The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of high-dimensional convex bodies. This conceptually simplifies the counterexample by Hayden-Winter to the additivity conjecture for the minimal output p-Renyi entropy (for p>1). Archive classification: quant-ph math.FA Remarks: 7 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.1189 or http://arXiv.org/abs/0910.1189 or by email in unzipped form by transmitting an empty message with subject line uget 0910.1189 or in gzipped form by using subject line get 0910.1189 to: math(a)arXiv.org.

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Abstract of a paper by Rui Liu
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "On shrinking and boundedly complete schauder frames of Banach spaces" by Rui Liu. Abstract: This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames. Archive classification: math.FA The source file(s), RuiLiu10.16.tex: 53807 bytes, is(are) stored in gzipped form as 0910.3369.gz with size 15kb. The corresponding postcript file has gzipped size 112kb. Submitted from: leorui(a)mail.nankai.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3369 or http://arXiv.org/abs/0910.3369 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3369 or in gzipped form by using subject line get 0910.3369 to: math(a)arXiv.org.

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Abstract of a paper by Romain Tessera
by alspach＠fourier.math.okstate.edu 27 Oct '09

27 Oct '09

This is an announcement for the paper "The inclusion of the Schur algebra in B(l^2) is not inverse-closed" by Romain Tessera. Abstract: The Schur algebra is the algebra of operators which are bounded on l^1 and on l^{\infty}. Q. Sun conjectured that the Schur algebra is inverse-closed. In this note, we disprove this conjecture. Precisely, we exhibit an operator in the Schur algebra, invertible in l^2, whose inverse is not bounded on l^1 nor on l^{\infty}. Archive classification: math.FA math.MG Mathematics Subject Classification: 47B38, 47B37 Remarks: 3 pages The source file(s), Schuralgebra.tex: 6835 bytes, is(are) stored in gzipped form as 0910.3285.gz with size 3kb. The corresponding postcript file has gzipped size 44kb. Submitted from: tessera(a)phare.normalesup.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.3285 or http://arXiv.org/abs/0910.3285 or by email in unzipped form by transmitting an empty message with subject line uget 0910.3285 or in gzipped form by using subject line get 0910.3285 to: math(a)arXiv.org.

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Abstract of a paper by J. M. Almira
by alspach＠fourier.math.okstate.edu 16 Oct '09

16 Oct '09

This is an announcement for the paper "Characterization of approximation schemes satisfying Shapiro's theorem" by J. M. Almira. Abstract: In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and n-term approximation for several dictionaries and norms. Moreover, we compare our main theorem with a classical result by Yu. Brundyi and we show two examples of approximation schemes that do not satisfy Shapiro's theorem. Archive classification: math.CA math.FA The source file(s), almira_shapiro_theorem.tex: 47247 bytes, is(are) stored in gzipped form as 0910.2826.gz with size 14kb. The corresponding postcript file has gzipped size . Submitted from: jmalmira(a)ujaen.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.2826 or http://arXiv.org/abs/0910.2826 or by email in unzipped form by transmitting an empty message with subject line uget 0910.2826 or in gzipped form by using subject line get 0910.2826 to: math(a)arXiv.org.

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Banach October 2009