Banach April 2007

banach@mathdept.okstate.edu

1 participants
4 discussions

Abstract of a paper by Florent Baudier
by Dale Alspach 17 Apr '07

17 Apr '07

This is an announcement for the paper "Metrical characterization of super-reflexivity and linear type of Banach spaces" by Florent Baudier. Abstract: We prove that a Banach space X is not super-reflexive if and only if the hyperbolic infinite tree embeds metrically into X. We improve one implication of J.Bourgain's result who gave a metrical characterization of super-reflexivity in Banach spaces in terms of uniforms embeddings of the finite trees. A characterization of the linear type for Banach spaces is given using the embedding of the infinite tree equipped with a suitable metric. Archive classification: Mathematics Subject Classification: 46B20; 51F99 Remarks: to appear in Archiv der Mathematik The source file(s), , is(are) stored in gzipped form as 0704.1955.gz with size 8kb. The corresponding postcript file has gzipped size 78kb. Submitted from: florent.baudier(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math(a)arXiv.org.

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Abstract of a paper by Valentin Ferenczi and Eloi Medina Galego
by Dale Alspach 17 Apr '07

17 Apr '07

This is an announcement for the paper "Even infinite dimensional real Banach spaces" by Valentin Ferenczi and Eloi Medina Galego. Abstract: This article is a continuation of a paper of the first author \cite{F} about complex structures on real Banach spaces. We define a notion of even infinite dimensional real Banach space, and prove that there exist even spaces, including HI or unconditional examples from \cite{F} and $C(K)$ examples due to Plebanek \cite{P}. We extend results of \cite{F} relating the set of complex structures up to isomorphism on a real space to a group associated to inessential operators on that space, and give characterizations of even spaces in terms of this group. We also generalize results of \cite{F} about totally incomparable complex structures to essentially incomparable complex structures, while showing that the complex version of a space defined by S. Argyros and A. Manoussakis \cite{AM} provide examples of essentially incomparable complex structures which are not totally incomparable. Archive classification: Mathematics Subject Classification: 46B03; 47A53. Remarks: 22 pages The source file(s), , is(are) stored in gzipped form as 0704.1459.gz with size 16kb. The corresponding postcript file has gzipped size 85kb. Submitted from: ferenczi(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math(a)arXiv.org.

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Abstract of a paper by Jesus Araujo
by Dale Alspach 10 Apr '07

10 Apr '07

This is an announcement for the paper "Examples and counterexamples of type I isometric shifts" by Jesus Araujo. Abstract: We provide examples of nonseparable spaces $X$ for which $C(X)$ admits an isometric shift of type I, which solves in the negative a problem proposed by Gutek {\em et al.} (J. Funct. Anal. {\bf 101} (1991), 97-119). We also give two independent methods for obtaining separable examples. The first one allows us in particular to construct examples with infinitely many nonhomeomorphic components in a subset of the Hilbert space $\ell^2$. The second one applies for instance to sequences adjoined to any $n$-dimensional compact manifold (for $n \ge 2$) or to the Sierpi\'nski curve. The combination of both techniques lead to different examples involving a convergent sequence adjoined to the Cantor set: one method for the case when the sequence converges to a point in the Cantor set, and the other one for the case when it converges outside. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: Primary 47B38; Secondary 46E15, 47B33, 47B37, 54D65, 54H20 Remarks: 41 pages. No figures. AMS-LaTeX The source file(s), shiftnum86.tex: 124237 bytes, is(are) stored in gzipped form as 0703892.gz with size 34kb. The corresponding postcript file has gzipped size 210kb. Submitted from: araujoj(a)unican.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0703892 or http://arXiv.org/abs/math.FA/0703892 or by email in unzipped form by transmitting an empty message with subject line uget 0703892 or in gzipped form by using subject line get 0703892 to: math(a)arXiv.org.

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Abstract of a paper by Boris Rubin
by Dale Alspach 10 Apr '07

10 Apr '07

This is an announcement for the paper "Intersection bodies and generalized cosine transforms" by Boris Rubin. Abstract: Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is interrelation between generalized cosine transforms of different kinds and their application to investigation of certain family of intersection bodies, which we call lambda-intersection bodies. The latter include k-intersection bodies (in the sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of $L_p$-spaces. In particular, we show that restriction of the spherical Radon transforms and the generalized cosine transforms onto lower dimensional subspaces preserves their integral-geometric structure. We apply this result to the study of sections of lambda-intersection bodies. A number of new characterizations of this class of bodies and examples are given. Archive classification: Mathematics Subject Classification: 44A12; 52A38 Remarks: 36 pages The source file(s), , is(are) stored in gzipped form as 0704.0061.gz with size 31kb. The corresponding postcript file has gzipped size 195kb. Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/ or http://arXiv.org/abs/ or by email in unzipped form by transmitting an empty message with subject line uget or in gzipped form by using subject line get to: math(a)arXiv.org.

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Banach April 2007