Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Stephan Fackler
by alspach＠math.okstate.edu 26 Oct '12

26 Oct '12

This is an announcement for the paper "The Kalton-Lancien theorem revisited: Maximal regularity does not extrapolate" by Stephan Fackler. Abstract: We give a new more explicit proof of a result by Kalton & Lancien stating that on each Banach space with an unconditional basis not isomorphic to a Hilbert space there exists a generator of a holomorphic semigroup which does not have maximal regularity. In particular, we show that there always exists a Schauder basis (f_m) such that the generator is a Schauder multiplier associated to the sequence (2^m). Moreover, we show that maximal regularity does not extrapolate: we construct consistent holomorphic semigroups (T_p(t)) on L^p for p in (1, \infty) which have maximal regularity if and only if p = 2. These assertions were both open problems. Our approach is completely different than the one of Kalton & Lancien. We use the characterization of maximal regularity by R-sectoriality for our construction. Archive classification: math.FA math.AP Mathematics Subject Classification: 35K90, 47D06 (Primary) 46B15 (Secondary) Remarks: 16 pages Submitted from: stephan.fackler(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.4333 or http://arXiv.org/abs/1210.4333

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Abstract of a paper by Philip A.H. Brooker
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,\alpha])$" by Philip A.H. Brooker. Abstract: Let $\alpha$ be an infinite ordinal and $\gamma$ the unique ordinal satisfying $\omega^{\omega^\gamma}\leq \alpha < \omega^{\omega^{\gamma+1}}$. We show that the Banach space $C([0,\,\alpha])$ of all continuous scalar-valued functions on the compact ordinal interval $[0,\,\alpha]$ has Szlenk index equal to $\omega^{\gamma+1}$ and $w^\ast$-dentability index equal to $\omega^{1+\gamma+1}$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B20 Submitted from: philip.a.h.brooker(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.3696 or http://arXiv.org/abs/1210.3696

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Abstract of a paper by Geraldo Botelho, Daniel Pellegrino, and Pilar Rueda
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "On Pietsch measures for summing operators and dominated polynomials" by Geraldo Botelho, Daniel Pellegrino, and Pilar Rueda. Abstract: We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials. Archive classification: math.FA Mathematics Subject Classification: 28C15, 46G25, 47B10, 47L22 Remarks: 13 pages Submitted from: pilar.rueda(a)uv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.3332 or http://arXiv.org/abs/1210.3332

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Abstract of a paper by S.A. Argyros, A. Manoussakis, and M. Petrakis
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Function spaces not containing $\ell_{1}$" by S.A. Argyros, A. Manoussakis, and M. Petrakis. Abstract: For $\Omega$ bounded and open subset of $\mathbb{R}^{d_{0}}$ and $X$ a reflexive Banach space with $1$-symmetric basis, the function space $JF_{X}(\Omega)$ is defined. This class of spaces includes the classical James function space. Every member of this class is separable and has non-separable dual. We provide a proof of topological nature that $JF_{X}(\Omega)$ does not contain an isomorphic copy of $\ell_{1}$. We also investigate the structure of these spaces and their duals. Archive classification: math.FA Mathematics Subject Classification: 46B10 Citation: Israel Journal of Mathematics 135 (2003), 29-81 Submitted from: amanousakis(a)isc.tuc.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.2379 or http://arXiv.org/abs/1210.2379

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Abstract of a paper by Henning Kempka and Jan Vybiral
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Lorentz spaces with variable exponents" by Henning Kempka and Jan Vybiral. Abstract: We introduce Lorentz spaces $L_{p(\cdot),q}(\R^n)$ and $L_{p(\cdot),q(\cdot)}(\R^n)$ with variable exponents. We prove several basic properties of these spaces including embeddings and the identity $L_{p(\cdot),p(\cdot)}(\R^n)=L_{p(\cdot)}(\R^n)$. We also show that these spaces arise through real interpolation between $L_{\p}(\R^n)$ and $L_\infty(\R^n)$. Furthermore, we answer in a negative way the question posed in \cite{DHN} whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability. Archive classification: math.FA Submitted from: henning.kempka(a)uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1738 or http://arXiv.org/abs/1210.1738

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Abstract of a paper by E.Ostrovsky and L.Sirota
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)" by E.Ostrovsky and L.Sirota. Abstract: We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate also a conjugate to offered spaces and obtain some embedding theorems. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables). Archive classification: math.FA math.PR Submitted from: leos(a)post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1168 or http://arXiv.org/abs/1210.1168

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Abstract of a paper by Jan-David Hardtke
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "On convergence with respect to an ideal and a family of matrices" by Jan-David Hardtke. Abstract: Recently P. Das, S. Dutta and E. Savas introduced and studied the notions of strong $A^I$-summability with respect to an Orlicz function $F$ and $A^I$-statistical convergence, where $A$ is a non-negative regular matrix and $I$ is an ideal on the set of natural numbers. In this note, we will generalise these notions by replacing $A$ with a family of matrices and $F$ with a family of Orlicz functions or moduli and study the thus obtained convergence methods. We will also give an application in Banach space theory, presenting a generalisation of Simons' $\sup$-$\limsup$-theorem to the newly introduced convergence methods (for the case that the filter generated by the ideal $I$ has a countable base), continuing the author's previous work. Archive classification: math.FA Mathematics Subject Classification: 40C05, 40C99, 46B20 Remarks: 32 pages Submitted from: hardtke(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.1350 or http://arXiv.org/abs/1210.1350

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Abstract of a paper by Costas Poulios
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Non-separable tree-like Banach spaces and Rosenthal's $\ell_1$-theorem " by Costas Poulios. Abstract: We introduce and investigate a class of non-separable tree-like Banach spaces. As a consequence, we prove that we can not achieve a satisfactory extension of Rosenthal's $\ell_1$-theorem to spaces of the type $\ell_1(\kappa)$, for $\kappa$ an uncountable cardinal. Archive classification: math.FA Mathematics Subject Classification: 46B25, 46B26 Submitted from: k-poulios(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.0792 or http://arXiv.org/abs/1210.0792

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Abstract of a paper by Florent P. Baudier
by alspach＠math.okstate.edu 16 Oct '12

16 Oct '12

This is an announcement for the paper "Quantitative nonlinear embeddings into Lebesgue sequence spaces" by Florent P. Baudier. Abstract: In this paper coarse, uniform and strong embeddings of metric spaces into Lebesgue sequence spaces are studied in their quantitative aspects. In particular, strong deformation gaps are obtained when embedding strongly a Hilbert space into $\ell_p$ for $0<p< 2$ as well as new insights on the nonlinear geometry of the spaces $L_p$ and $\ell_p$ for $0<p<1$. The exact $\ell_q$-compression of $\ell_p$-spaces is computed. Finally the coarse deformation of metric spaces with property A and amenable groups is investigated. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20, 46B85, 46T99, 20F65 Submitted from: florent(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1210.0588 or http://arXiv.org/abs/1210.0588

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Abstract of a paper by Alexander E. Litvak, Mark Rudelson, and Nicole Tomczak-Jaegermann
by alspach＠math.okstate.edu 28 Sep '12

28 Sep '12

This is an announcement for the paper "On approximations by projections of polytopes with few facets" by Alexander E. Litvak, Mark Rudelson, and Nicole Tomczak-Jaegermann. Abstract: We provide an affirmative answer to a problem posed by Barvinok and Veomett, showing that in general an n-dimensional convex body cannot be approximated by a projection of a section of a simplex of a sub-exponential dimension. Moreover, we establish a lower bound of the Banach-Mazur distance between n-dimensional projections of sections of an N-dimensional simplex and a certain convex symmetric body, which is sharp up to a logarithmic factor for all N>n. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 52A23, 52A27, Secondary: 52B55, 46B09 Remarks: 22 pages Submitted from: rudelson(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1209.6281 or http://arXiv.org/abs/1209.6281

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