- Banach - mathdept.okstate.edu

Abstract of a paper by Spiros A. Argyros and Theocharis Raikoftsalis
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "The cofinal property of the reflexive indecomposable Banach spaces" by Spiros A. Argyros and Theocharis Raikoftsalis. Abstract: It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell_p$ saturated space with $1<p<\infty$ and of a $c_0$ saturated space. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B06, 46B70 Remarks: 29 pages The source file(s), Arg-Raiko-Cofinal.tex: 122453 bytes, is(are) stored in gzipped form as 1003.0870.gz with size 36kb. The corresponding postcript file has gzipped size 84kb. Submitted from: sargyros(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.0870 or http://arXiv.org/abs/1003.0870 or by email in unzipped form by transmitting an empty message with subject line uget 1003.0870 or in gzipped form by using subject line get 1003.0870 to: math(a)arXiv.org.

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Abstract of a paper by I. Gasparis, M.K. Papadiamantis and D.Z. Zisimopoulou
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "More $\ell_r$ saturated $\mathcal{L}_\infty$ spaces" by I. Gasparis, M.K. Papadiamantis and D.Z. Zisimopoulou. Abstract: We present some new examples of separable $\mathcal_\infty$ spaces which are $\ell_r$ saturated for some $1 < r < \infty$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 05D10 The source file(s), lrsaturatedtel.tex: 49218 bytes, is(are) stored in gzipped form as 1003.0579.gz with size 15kb. The corresponding postcript file has gzipped size 84kb. Submitted from: ioagaspa(a)math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.0579 or http://arXiv.org/abs/1003.0579 or by email in unzipped form by transmitting an empty message with subject line uget 1003.0579 or in gzipped form by using subject line get 1003.0579 to: math(a)arXiv.org.

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Abstract of a paper by Ohad Giladi, Manor Mendel, and Assaf Naor
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "Improved bounds in the metric cotype inequality for Banach spaces" by Ohad Giladi, Manor Mendel, and Assaf Naor. Abstract: It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m< n^{1+1/q}$ such that for every f:Z_m^n --> X we have \sum_{j=1}^n \Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] < C m^q \Avg_{\e,x} [ ||f(x+\e)-f(x) ||_X^q ], where the expectations are with respect to uniformly chosen x\in Z_m^n and \e\in \{-1,0,1\}^n, and all the implied constants may depend only on q and the Rademacher cotype q constant of X. This improves the bound of m< n^{2+\frac{1}{q}} from [Mendel, Naor 2008]. The proof of the above inequality is based on a ``smoothing and approximation" procedure which simplifies the proof of the metric characterization of Rademacher cotype of [Mendel, Naor 2008]. We also show that any such ``smoothing and approximation" approach to metric cotype inequalities must require m> n^{(1/2)+(1/q)}. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B80,46B85,51F99,05C12 Remarks: 27 pages, 1 figure The source file(s), cotypeGMN.bbl: 3212 bytes cotypeGMN.tex: 87911 bytes tr-jigsaw.eps: 52290 bytes tr-jigsaw.pdf: 28339 bytes, is(are) stored in gzipped form as 1003.0279.tar.gz with size 80kb. The corresponding postcript file has gzipped size 84kb. Submitted from: mendelma(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.0279 or http://arXiv.org/abs/1003.0279 or by email in unzipped form by transmitting an empty message with subject line uget 1003.0279 or in gzipped form by using subject line get 1003.0279 to: math(a)arXiv.org.

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Abstract of a paper by Oleg Reinov and Qaisar Latif
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "Banach spaces without approximation properties of type p" by Oleg Reinov and Qaisar Latif. Abstract: The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a negative answer, and that the answer was known, essentially, in 1985 after the papers "Approximation properties of order p and the existence of non-p-nuclear operators with p-nuclear second adjoints" (Math. Nachr. 109(1982), 125-134) and "Approximation of operators in Banach spaces" (Application of functional analysis in the approximation theory (KGU, Kalinin), 1985, 128-142) by Reinov O.I. have been appeared in 1982 and in 1985 respectively. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: LATeX, English (4 pp.) The source file(s), FA_J_LAT.tex: 15882 bytes, is(are) stored in gzipped form as 1003.0085.gz with size 6kb. The corresponding postcript file has gzipped size 84kb. Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1003.0085 or http://arXiv.org/abs/1003.0085 or by email in unzipped form by transmitting an empty message with subject line uget 1003.0085 or in gzipped form by using subject line get 1003.0085 to: math(a)arXiv.org.

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Abstract of a paper by Mehmet Orhon
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "The ideal center of the dual of a Banach lattice" by Mehmet Orhon. Abstract: Let $E$ be a Banach lattice. Its ideal center $Z(E)$ is embedded naturally in the ideal center $Z(E')$ of its dual. The embedding may be extended to a contractive algebra and lattice homomorphism of $Z(E)''$ into $Z(E')$. We show that the extension is onto $Z(E')$ if and only if $E$ has a topologically full center. (That is, for each $x\in E$, the closure of $Z(E)x$ is the closed ideal generated by $x$.) The result can be generalized to the ideal center of the order dual of an Archimedean Riesz space and in a modified form to the orthomorphisms on the order dual of an Archimedean Riesz space. Archive classification: math.FA Mathematics Subject Classification: 47B38 The source file(s), center-final.tex: 25459 bytes, is(are) stored in gzipped form as 1002.4346.gz with size 8kb. The corresponding postcript file has gzipped size 84kb. Submitted from: mo(a)unh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.4346 or http://arXiv.org/abs/1002.4346 or by email in unzipped form by transmitting an empty message with subject line uget 1002.4346 or in gzipped form by using subject line get 1002.4346 to: math(a)arXiv.org.

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Abstract of a paper by Mar Jimenez-Sevilla and Luis Sanchez-Gonzalez
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "Smooth extension of functions on non-separable Banach spaces" by Mar Jimenez-Sevilla and Luis Sanchez-Gonzalez. Abstract: Let us consider a Banach space $X$ with the property that every Lipschitz function can be uniformly approximated by Lipschitz and $C^1$-smooth functions (this is the case either for a weakly compactly generated Banach space $X$ with a $C^1$-smooth norm, or a Banach space $X$ bi-Lipschitz homeomorphic to a subset of $c_0(\Gamma)$, for some set $\Gamma$, such that the coordinate functions of the homeomorphism are $C^1$-smooth). Then for every closed subspace $Y\subset X$ and every $C^1$-smooth (Lipschitz) function $f:Y\to\Real$, there is a $C^1$-smooth (Lipschitz, repectively) extension of $f$ to $X$. An analogous result can be stated for real-valued functions defined on closed convex subsets of $X$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 12 pages The source file(s), draftSmoothextension220210.tex: 59770 bytes, is(are) stored in gzipped form as 1002.4147.gz with size 15kb. The corresponding postcript file has gzipped size 84kb. Submitted from: lfsanche(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.4147 or http://arXiv.org/abs/1002.4147 or by email in unzipped form by transmitting an empty message with subject line uget 1002.4147 or in gzipped form by using subject line get 1002.4147 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 22 Mar '10

22 Mar '10

This is an announcement for the paper "Natural symmetric tensor norms" by Daniel Carando and Daniel Galicer. Abstract: In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. We prove that there are exactly six natural symmetric tensor norms for $n\ge 3$, a noteworthy difference with the 2-fold case in which there are four. Using a symmetric version of a result of Carne we also describe which natural symmetric tensor norms preserve Banach algebras. Archive classification: math.FA Mathematics Subject Classification: 46M05 Remarks: 11 pages The source file(s), Natural22.tex: 42738 bytes, is(are) stored in gzipped form as 1002.3950.gz with size 12kb. The corresponding postcript file has gzipped size 84kb. 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/1002.3950 or http://arXiv.org/abs/1002.3950 or by email in unzipped form by transmitting an empty message with subject line uget 1002.3950 or in gzipped form by using subject line get 1002.3950 to: math(a)arXiv.org.

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Abstract of a paper by Oleg I. Reinov
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "Approximation of operators in Banach spaces" by Oleg I. Reinov. Abstract: It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we investigate some properties of the space Pi_p, related to this new topology. 2010-remark: Occasionally, the topology is coincides with the lambda_p-topology from the paper "Compact operators which factor through subspaces of l_p", Math. Nachr. 281(2008), 412-423 by Deba Prasad Sinha and Anil Kumar Karn. Archive classification: math.FA Mathematics Subject Classification: 46B28 Citation: In the collection "Primenenie funkcional'nogo analiza v teorii The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.3902 or http://arXiv.org/abs/1002.3902 or by email in unzipped form by transmitting an empty message with subject line uget 1002.3902 or in gzipped form by using subject line get 1002.3902 to: math(a)arXiv.org.

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Abstract of a paper by Rui Liu and Bentuo Zheng
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "A characterization of Schauder frames which are near-Schauder bases" by Rui Liu and Bentuo Zheng. Abstract: A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases. Archive classification: math.FA Mathematics Subject Classification: Primary 46B15, 46B45; Secondary 47A20. Remarks: 12 pages The source file(s), LZh.tex: 37398 bytes, is(are) stored in gzipped form as 1002.3851.gz with size 11kb. The corresponding postcript file has gzipped size 84kb. 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/1002.3851 or http://arXiv.org/abs/1002.3851 or by email in unzipped form by transmitting an empty message with subject line uget 1002.3851 or in gzipped form by using subject line get 1002.3851 to: math(a)arXiv.org.

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Abstract of a paper by Tuomas Hyt\"onen and Mikko Kemppainen
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry" by Tuomas Hyt\"onen and Mikko Kemppainen. Abstract: Hyt\"onen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type p property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 42B25 (Primary) 46E40 (Secondary) Remarks: 10 pages The source file(s), carleson.bbl: 2240 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.2876 or http://arXiv.org/abs/1002.2876 or by email in unzipped form by transmitting an empty message with subject line uget 1002.2876 or in gzipped form by using subject line get 1002.2876 to: math(a)arXiv.org.

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