- Banach - mathdept.okstate.edu

Abstract of a paper by Boris Burshteyn
by alspach＠fourier.math.okstate.edu 19 Feb '09

19 Feb '09

This is an announcement for the paper "Strictly singular uniform $\lambda-$adjustment in Banach spaces" by Boris Burshteyn. Abstract: Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators in Banach spaces and prove theorems about lower semi--Fredholm stability. We also state some new open questions related to strict singularity and the geometry of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55; 47B07 Remarks: 23 pages The source file(s), boris997paper2.tex: 117155 bytes, is(are) stored in gzipped form as 0902.3045.gz with size 24kb. The corresponding postcript file has gzipped size . Submitted from: boris997(a)astound.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.3045 or http://arXiv.org/abs/0902.3045 or by email in unzipped form by transmitting an empty message with subject line uget 0902.3045 or in gzipped form by using subject line get 0902.3045 to: math(a)arXiv.org.

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Abstract of a paper by Volker Thuerey
by alspach＠fourier.math.okstate.edu 19 Feb '09

19 Feb '09

This is an announcement for the paper "Angles and polar coordinates in real normed spaces" by Volker Thuerey. Abstract: We try to create a wise definition of 'angle spaces'. Based on an idea of Ivan Singer, we introduce a new concept of an angle in real Banach spaces, which generalizes the euclidean angle in Hilbert spaces. With this angle it is shown that in every two-dimensional subspace of a real Banach space we can describe elements uniquely by polar coordinates. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A10 Remarks: 21 pages, 8 figures The source file(s), anglepaper.tex: 114700 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.2731 or http://arXiv.org/abs/0902.2731 or by email in unzipped form by transmitting an empty message with subject line uget 0902.2731 or in gzipped form by using subject line get 0902.2731 to: math(a)arXiv.org.

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Abstract of a paper by Pascal Lefevre, Daniel Li, and Herve Queffelec , Luis Rodriguez-Piazza
by alspach＠fourier.math.okstate.edu 19 Feb '09

19 Feb '09

This is an announcement for the paper "Thin sets of integers in Harmonic analysis and p-stable random Fourier series" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza. Abstract: We investigate the behavior of some thin sets of integers defined through random trigonometric polynomial when one replaces Gaussian or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in one case this behavior is essentially the same as in the Gaussian case, whereas in another case, this behavior is entirely different. Archive classification: math.FA Mathematics Subject Classification: Primary: 43A46 ; secondary: 42A55; 42A61; 60G52 The source file(s), p-stableBETISfinale.tex: 72111 bytes, is(are) stored in gzipped form as 0902.2625.gz with size 21kb. The corresponding postcript file has gzipped size 143kb. Submitted from: lefevre(a)euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.2625 or http://arXiv.org/abs/0902.2625 or by email in unzipped form by transmitting an empty message with subject line uget 0902.2625 or in gzipped form by using subject line get 0902.2625 to: math(a)arXiv.org.

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Abstract of a paper by Jihoon Lee, Paul F. X. Mueller and Stefan Mueller
by alspach＠fourier.math.okstate.edu 19 Feb '09

19 Feb '09

This is an announcement for the paper "Compensated compactness, separately convex functions and interpolatory estimates between Riesz transforms and Haar projections" by Jihoon Lee, Paul F. X. Mueller and Stefan Mueller . Abstract: We prove sharp interpolatory estimates between Riesz Transforms and directional Haar projections. We obtain applications to the theory of compensated compactness and prove a conjecture of L. Tartar on semi-continuity of separately convex integrands. Archive classification: math.FA Mathematics Subject Classification: 49J45; 42C15; 35B35 The source file(s), lmm.bbl: 4934 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.2102 or http://arXiv.org/abs/0902.2102 or by email in unzipped form by transmitting an empty message with subject line uget 0902.2102 or in gzipped form by using subject line get 0902.2102 to: math(a)arXiv.org.

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Abstract of a paper by M.I. Ostrovskii, V.S. Shulman, and L. Turowska
by alspach＠fourier.math.okstate.edu 19 Feb '09

19 Feb '09

This is an announcement for the paper "Fixed points of groups of biholomorphic transformations of operator balls using the midpoint property" by M.I. Ostrovskii, V.S. Shulman, and L. Turowska. Abstract: A new techniques for proving the existence of fixed points of groups of isometric transformations is developed. It is used to find simpler proofs and real-case versions of previous results of the authors. In particular, we use the obtained fixed point theorem to show that a bounded representation in a separable, real or complex, Hilbert space which has an invariant indefinite quadratic form with finitely many negative squares is orthogonalizable or unitarizable (equivalent to an orthogonal or unitary representation), respectively. Archive classification: math.MG math.OA Mathematics Subject Classification: 47H10; 47B50; 22D10; 54E35 The source file(s), midpoints10.tex: 42873 bytes, is(are) stored in gzipped form as 0902.1784.gz with size 14kb. The corresponding postcript file has gzipped size 109kb. Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.1784 or http://arXiv.org/abs/0902.1784 or by email in unzipped form by transmitting an empty message with subject line uget 0902.1784 or in gzipped form by using subject line get 0902.1784 to: math(a)arXiv.org.

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Abstract of a paper by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias
by alspach＠fourier.math.okstate.edu 11 Feb '09

11 Feb '09

This is an announcement for the paper "Hereditarily indecomposable Banach algebras of diagonal operators" by Spiros A. Argyros, Irene Deliyanni, and Andreas G. Tolias. Abstract: We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every $T\in \mathcal{L}_{diag}({\mathfrak X}_D)$ is of the form $T=\lambda I+K$, where $K$ is a compact operator. Archive classification: math.FA Mathematics Subject Classification: 46B28, 47L10, 46B20, 46B03. Remarks: 35 pages, submitted for publication to Israel J. Math The source file(s), HI_DIAG.tex.bak: 124849 bytes, is(are) stored in gzipped form as 0902.1646.gz with size 33kb. The corresponding postcript file has gzipped size 188kb. 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/0902.1646 or http://arXiv.org/abs/0902.1646 or by email in unzipped form by transmitting an empty message with subject line uget 0902.1646 or in gzipped form by using subject line get 0902.1646 to: math(a)arXiv.org.

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Abstract of a paper by Emanuel Milman
by alspach＠fourier.math.okstate.edu 11 Feb '09

11 Feb '09

This is an announcement for the paper "Isoperimetric and concentration inequalities - Part I: Equivalence under curvature lower bound" by Emanuel Milman. Abstract: It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the measure of sets separated from sets having half the total measure, as a function of their mutual distance. We show that under a lower bound condition on the Bakry--\'Emery curvature tensor of a Riemannian manifold equipped with a density, completely general concentration inequalities imply back their isoperimetric counterparts, up to dimension \emph{independent} bounds. As a corollary, we can recover and extend all previously known (dimension dependent) results by generalizing an isoperimetric inequality of Bobkov, and provide a new proof that under natural convexity assumptions, arbitrarily weak concentration implies a dimension independent linear isoperimetric inequality. Further applications will be described in a subsequent work. Contrary to previous attempts in this direction, our method is entirely geometric, continuing the approach set forth by Gromov and adapted to the manifold-with-density setting by Morgan. Archive classification: math.DG math.FA Remarks: 30 pages; second part involving numerous applications will appear The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.1560 or http://arXiv.org/abs/0902.1560 or by email in unzipped form by transmitting an empty message with subject line uget 0902.1560 or in gzipped form by using subject line get 0902.1560 to: math(a)arXiv.org.

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Abstract of a paper by Paul F. X. Mueller
by alspach＠fourier.math.okstate.edu 11 Feb '09

11 Feb '09

This is an announcement for the paper "Extrapolation of vector valued rearrangment operators II" by Paul F. X. Mueller. Abstract: We determine the extrapolation law for rearrangement operators of the Haar system on vector valued Hardy spaces. Archive classification: math.FA Mathematics Subject Classification: 46B42, 46B70, 47B37 The source file(s), pfxm_2009.bbl: 3113 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.1330 or http://arXiv.org/abs/0902.1330 or by email in unzipped form by transmitting an empty message with subject line uget 0902.1330 or in gzipped form by using subject line get 0902.1330 to: math(a)arXiv.org.

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Abstract of a paper by Gelu Popescu
by alspach＠fourier.math.okstate.edu 11 Feb '09

11 Feb '09

This is an announcement for the paper "Noncommutative hyperbolic geometry on the unit ball of $B(H)^n$" by Gelu Popescu. Abstract: In this paper we introduce a hyperbolic distance $\delta$ on the noncommutative open ball $[B(H)^n]_1$, where $B(H)$ is the algebra of all bounded linear operators on a Hilbert space $H$, which is a noncommutative extension of the Poincare-Bergman metric on the open unit ball of $C^n$. We prove that $\delta$ is invariant under the action of the group $Aut([B(H)^n]_1)$ of all free holomorphic automorphisms of $[B(\cH)^n]_1$, and show that the $\delta$-topology and the usual operator norm topology coincide on $[B(H)^n]_1$. Moreover, we prove that $[B(H)^n]_1$ is a complete metric space with respect to the hyperbolic metric and obtained an explicit formula for $\delta$ in terms of the reconstruction operator. A Schwarz-Pick lemma for bounded free holomorphic functions on $[B(H)^n]_1$, with respect to the hyperbolic metric, is also obtained. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L52; 32F45; 47L25; 32Q45 Remarks: 29 pages, to appear in J. Funct. Anal The source file(s), hyperbolic.tex: 116240 bytes, is(are) stored in gzipped form as 0810.0644.gz with size 30kb. The corresponding postcript file has gzipped size 78kb. Submitted from: gelu.popescu(a)utsa.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0810.0644 or http://arXiv.org/abs/0810.0644 or by email in unzipped form by transmitting an empty message with subject line uget 0810.0644 or in gzipped form by using subject line get 0810.0644 to: math(a)arXiv.org.

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Abstract of a paper by Fernando Rambla-Barreno and Jarno Talponen
by alspach＠fourier.math.okstate.edu 11 Feb '09

11 Feb '09

This is an announcement for the paper "Uniformly convex-transitive function spaces" by Fernando Rambla-Barreno and Jarno Talponen. Abstract: We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B20; 46B25 The source file(s), RotCad_acc.tex: 46198 bytes, is(are) stored in gzipped form as 0902.0640.gz with size 14kb. The corresponding postcript file has gzipped size 99kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.0640 or http://arXiv.org/abs/0902.0640 or by email in unzipped form by transmitting an empty message with subject line uget 0902.0640 or in gzipped form by using subject line get 0902.0640 to: math(a)arXiv.org.

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