Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Kevin Beanland, Ryan Causey, Daniel Freeman, and Ben Wallis
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "Class of operators determined by ordinal indices" by Kevin Beanland, Ryan Causey, Daniel Freeman, and Ben Wallis. Abstract: We introduce and study the Bourgain index of an operator between two Banach spaces. In particular, we study the Bourgain $\ell_p$ and $c_0$ indices of an operator. Several estimates for finite and infinite direct sums are established. We define classes determined by these indices and show that some of these classes form operator ideals. We characterize the ordinals which occur as the index of an operator and establish exactly when the defined classes are closed. We study associated indices for non-preservation of $\ell_p^\xi$ and $c_0^\xi$ spreading models and indices characterizing weak compactness of operators between separable Banach spaces. We also show that some of these classes are operator ideals and discuss closedness and distinctness of these classes. Archive classification: math.FA Mathematics Subject Classification: 46B28 Remarks: 45 pages Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.06285 or http://arXiv.org/abs/1507.06285

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Abstract of a paper by Richard Lechner and Markus Passenbrunner and Joscha Prochno
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "Estimating averages of order statistics of bivariate functions" by Richard Lechner and Markus Passenbrunner and Joscha Prochno. Abstract: We prove uniform estimates for the expected value of averages of order statistics of bivariate functions in terms of their largest values by a direct analysis. As an application, uniform estimates for the expected value of averages of order statistics of sequences of independent random variables in terms of Orlicz norms are obtained. In the case where the bivariate functions are matrices, we provide a ``minimal'' probability space which allows us to $C$-embed certain Orlicz spaces $\ell_M^n$ into $\ell_1^{cn^3}$, $c,C>0$ being absolute constants. Archive classification: math.PR math.FA math.ST stat.TH Submitted from: joscha.prochno(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.06227 or http://arXiv.org/abs/1507.06227

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Abstract of a paper by Fernando Albiac, Jose L. Ansorena, Oscar Ciaurri and Juan L. Varona
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "Unconditional and quasi-greedy bases in $L_p$ with applications to Jacobi polynomials Fourier series" by Fernando Albiac, Jose L. Ansorena, Oscar Ciaurri and Juan L. Varona. Abstract: We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in $L_p$ does not converge unless $p=2$. As a by-product of our work on quasi-greedy bases in $L_{p}(\mu)$, we show that no normalized unconditional basis in $L_p$, $p\not=2$, can be semi-normalized in $L_q$ for $q\not=p$, thus extending a classical theorem of Kadets and Pe{\l}czy{\'n}ski from 1968. Archive classification: math.FA Mathematics Subject Classification: 46B15 (Primary) 41A65 (Secondary) Submitted from: joseluis.ansorena(a)unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.05934 or http://arXiv.org/abs/1507.05934

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Abstract of a paper by khalil saadi
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "On the composition ideals of Lipschitz mappings" by khalil saadi. Abstract: We study in this paper some property of Lipschitz mappings which admit factorization through an operator ideal. We try to construct Lipschitz cross-norms from known tensor norms in order to represent certain classes of Lipschitz mappings. Inspired by the definition of p-summing linear operators we introduce a new concpet in the the category of Lipschitz mappings that is called strictly Lipschitz p-summing. Archive classification: math.FA Mathematics Subject Classification: [2000] 47B10, 46B28, 47L20 Report Number: 21 pages Submitted from: kh_saadi(a)yahoo.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.05872 or http://arXiv.org/abs/1507.05872

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Abstract of a paper by Marek Cuth
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "Separable determination of (generalized-)lushness" by Marek Cuth. Abstract: We prove that every Asplund lush space is generalized-lush using the method of separable reduction. This gives a partial positive answer to a question by Jan-David Hardtke. Archive classification: math.FA Mathematics Subject Classification: 46B26, 46B20 Submitted from: cuth(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.05709 or http://arXiv.org/abs/1507.05709

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Abstract of a paper by G. Araujo, L. Bernal-Gonzalez, G.A. Munoz-Fernandez, J.A. Prado-Bassas and J.B. Seoane-Sepulveda
by alspach＠math.okstate.edu 23 Jul '15

23 Jul '15

This is an announcement for the paper "Lineability in sequence and function spaces" by G. Araujo, L. Bernal-Gonzalez, G.A. Munoz-Fernandez, J.A. Prado-Bassas and J.B. Seoane-Sepulveda. Abstract: It is proved the existence of large algebraic structures \break --including large vector subspaces or infinitely generated free algebras-- inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of non-continuous separately continuous real functions. Lineability in special spaces of sequences is also investigated. Some of our findings complete or extend a number of results by several authors. Archive classification: math.FA Mathematics Subject Classification: 28A20 Remarks: 18 pages, 1 figure Submitted from: bassas(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.04477 or http://arXiv.org/abs/1507.04477

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Abstract of a paper by Stefan Brach, Enrique A. Sanchez Perez and Dirk Werner
by alspach＠math.okstate.edu 16 Jul '15

16 Jul '15

This is an announcement for the paper "The Daugavet equation for bounded vector valued functions" by Stefan Brach, Enrique A. Sanchez Perez and Dirk Werner. Abstract: Requirements under which the Daugavet equation and the alternative Daugavet equation hold for pairs of nonlinear maps between Banach spaces are analysed. A geometric description is given in terms of nonlinear slices. Some local versions of these properties are also introduced and studied, as well as tests for checking if the required conditions are satisfied in relevant cases. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B25, 46B80 Submitted from: werner(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.04185 or http://arXiv.org/abs/1507.04185

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Abstract of a paper by Ondrej Kurka
by alspach＠math.okstate.edu 16 Jul '15

16 Jul '15

This is an announcement for the paper "Zippin's embedding theorem and amalgamations of classes of Banach" by Ondrej Kurka. Abstract: It was proved by Dodos and Ferenczi that the classes of Banach spaces with a separable dual and of separable reflexive Banach spaces are strongly bounded. In this note, we provide an isometric version of this result. Archive classification: math.FA Mathematics Subject Classification: 46B04, 54H05 (Primary) 46B10, 46B15, 46B70 (Secondary) Submitted from: kurka.ondrej(a)seznam.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.03899 or http://arXiv.org/abs/1507.03899

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Abstract of a paper by Ben Wallis
by alspach＠math.okstate.edu 16 Jul '15

16 Jul '15

This is an announcement for the paper "Closed ideals in $\mathcal{L}(X)$ and $\mathcal{L}(X^*)$ when $X$ contains certain copies of $\ell_p$ and $c_0$" by Ben Wallis. Abstract: Suppose $X$ is a real or complexified Banach space containing a complemented copy of $\ell_p$, $p\in(1,2)$, and a copy (not necessarily complemented) of either $\ell_q$, $q\in(p,\infty)$, or $c_0$. Then $\mathcal{L}(X)$ and $\mathcal{L}(X^*)$ each admit continuum many closed ideals. If in addition $q\geq p'$, $\frac{1}{p}+\frac{1}{p'}=1$, then the closed ideals of $\mathcal{L}(X)$ and $\mathcal{L}(X^*)$ each fail to be linearly ordered. We obtain additional results in the special cases of $\mathcal{L}(\ell_1\oplus\ell_q)$ and $\mathcal{L}(\ell_p\oplus c_0)$, $1<p<2<q<\infty$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 28 pages Submitted from: wallis(a)math.niu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.03241 or http://arXiv.org/abs/1507.03241

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Abstract of a paper by P. Rueda and E.A. Sanchez-Perez
by alspach＠math.okstate.edu 16 Jul '15

16 Jul '15

This is an announcement for the paper "The Dvoretsky-Rogers Theorem for vector valued integrals on function spaces" by P. Rueda and E.A. Sanchez-Perez. Abstract: We show a Dvoretsky-Rogers type Theorem for the adapted version of the $q$-summing operators to the topology of the convergence of the vector valued integrals on Banach function spaces. In the pursuit of this objective we prove that the mere summability of the identity map does not guaranty that the space has to be finite dimensional, contrarily to the classical case. Some local compactness assumptions on the unit balls are required. Our results open the door to new convergence theorems and tools regarding summability of series of integrable functions and approximation in function spaces, since we may find infinite dimensional spaces in which convergence of the integrals ---our vector valued version of convergence in the weak topology--- is equivalent to the convergence with respect to the norm. Examples and applications are also given. Archive classification: math.FA Mathematics Subject Classification: 46B15, 46B50, 46E30, 46G10 Submitted from: easancpe(a)mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.03033 or http://arXiv.org/abs/1507.03033

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