March 2010 - Banach - mathdept.okstate.edu

Abstract of a paper by Ellen Veomett and Kevin Wildrick
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "Spaces of small metric cotype" by Ellen Veomett and Kevin Wildrick. Abstract: Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result. Archive classification: math.MG math.FA Mathematics Subject Classification: 30L05; 46B85 Remarks: 21 pages The source file(s), MetricCotype8.bbl: 3780 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.3326 or http://arXiv.org/abs/1001.3326 or by email in unzipped form by transmitting an empty message with subject line uget 1001.3326 or in gzipped form by using subject line get 1001.3326 to: math(a)arXiv.org.

1 0

Abstract of a paper by F. Sukochev and D. Zanin
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces" by F. Sukochev and D. Zanin. Abstract: \begin{abstract} {\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $0<q<1$ for which $ \Vert \sum_{_{k=1}}^n\xi_k\Vert _{E}\leq Cn^{q}$, where $\{\xi_k\}_{k\ge 1}\subset E$ is an arbitrary sequence of independent identically distributed symmetric random variables on $[0,1]$ and $C>0$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces. \end{abstract} Archive classification: math.FA Mathematics Subject Classification: 46E30 (46B09 46B20) Citation: Studia Math. 191 (2009), no. 2, 101--122 The source file(s), sukochev_zanin_submitted.tex: 67832 bytes, is(are) stored in gzipped form as 1001.2432.gz with size 20kb. The corresponding postcript file has gzipped size 84kb. Submitted from: zani0005(a)csem.flinders.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.2432 or http://arXiv.org/abs/1001.2432 or by email in unzipped form by transmitting an empty message with subject line uget 1001.2432 or in gzipped form by using subject line get 1001.2432 to: math(a)arXiv.org.

1 0

Abstract of a paper by Nigel J. Kalton and Marisa Zymonopoulou
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "Positive definite distributions and normed spaces" by Nigel J. Kalton and Marisa Zymonopoulou. Abstract: We answer a question of Alex Koldobsky on isometric embeddings of finite dimensional normed spaces. Archive classification: math.FA Mathematics Subject Classification: 52A21 The source file(s), zymnotes4.tex: 71037 bytes, is(are) stored in gzipped form as 1001.1412.gz with size 21kb. The corresponding postcript file has gzipped size 84kb. Submitted from: marisa.zym(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.1412 or http://arXiv.org/abs/1001.1412 or by email in unzipped form by transmitting an empty message with subject line uget 1001.1412 or in gzipped form by using subject line get 1001.1412 to: math(a)arXiv.org.

1 0

Abstract of a paper by Enrique A. Sanchez Perez and Dirk Werner
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "The geometry of L^p-spaces over atomless measure spaces and the Daugavet property" by Enrique A. Sanchez Perez and Dirk Werner. Abstract: We show that $L^p$-spaces over atomless measure spaces can be characterized in terms of a $p$-concavity type geometric property that is related with the Daugavet property. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B25 The source file(s), LpDaugavet7.tex: 44923 bytes, is(are) stored in gzipped form as 1001.1262.gz with size 14kb. The corresponding postcript file has gzipped size 84kb. 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/1001.1262 or http://arXiv.org/abs/1001.1262 or by email in unzipped form by transmitting an empty message with subject line uget 1001.1262 or in gzipped form by using subject line get 1001.1262 to: math(a)arXiv.org.

1 0

Abstract of a paper by Matthew Daws
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "A bicommutant theorem for dual Banach algebras" by Matthew Daws. Abstract: A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism $\pi:\mc A\to\mc B(E)$ such that $\pi(\mc A)$ equals its own bicommutant. Archive classification: math.FA Mathematics Subject Classification: 46H05, 46H15, 47L10 Remarks: 6 pages The source file(s), dba.tex: 23544 bytes, is(are) stored in gzipped form as 1001.1146.gz with size 8kb. The corresponding postcript file has gzipped size 84kb. Submitted from: matt.daws(a)cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.1146 or http://arXiv.org/abs/1001.1146 or by email in unzipped form by transmitting an empty message with subject line uget 1001.1146 or in gzipped form by using subject line get 1001.1146 to: math(a)arXiv.org.

1 0

Abstract of a paper by Mathieu Meyer, Carsten Schutt and Elisabeth M. Werner
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "A convex body whose centroid and Santalo point are far apart" by Mathieu Meyer, Carsten Schutt and Elisabeth M. Werner. Abstract: We give an example of a convex body whose centroid and Santal\'o point are ``far apart". Archive classification: math.FA Mathematics Subject Classification: 52A20, 53A15 The source file(s), symmetrie25-12-09.tex: 65533 bytes, is(are) stored in gzipped form as 1001.0714.gz with size 16kb. The corresponding postcript file has gzipped size 84kb. Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0714 or http://arXiv.org/abs/1001.0714 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0714 or in gzipped form by using subject line get 1001.0714 to: math(a)arXiv.org.

1 0