September 2009 - Banach - mathdept.okstate.edu

Abstract of a paper by Joaquim Martin and Mario Milman
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "Pointwise symmetrization inequalities for Sobolev functions and applications" by Joaquim Martin and Mario Milman. Abstract: We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations Archive classification: math.FA math.AP The source file(s), martin-milman-symm.tex: 205567 bytes, is(are) stored in gzipped form as 0908.1751.gz with size 53kb. The corresponding postcript file has gzipped size 289kb. Submitted from: mario.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1751 or http://arXiv.org/abs/0908.1751 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1751 or in gzipped form by using subject line get 0908.1751 to: math(a)arXiv.org.

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Abstract of a paper by Kevin Beanland
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "An ordinal index on the space of strictly singular operators" by Kevin Beanland. Abstract: Using the notion of $S_\xi$-strictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is bounded by $\omega_1$. In particular, we apply this result to study operators on totally incomparable spaces, hereditarily indecomposable spaces and spaces with few operators. Archive classification: math.FA Mathematics Subject Classification: 46B28; 03E15 Remarks: 8 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1113 or http://arXiv.org/abs/0908.1113 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1113 or in gzipped form by using subject line get 0908.1113 to: math(a)arXiv.org.

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Abstract of a paper by Maxim V. Balashov and Dusan Repovs
by alspach＠fourier.math.okstate.edu 08 Sep '09

08 Sep '09

This is an announcement for the paper "Uniform convexity and the splitting problem for selections" by Maxim V. Balashov and Dusan Repovs. Abstract: We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60; 54C65; 52A07; 46A55; 52A01 Citation: J. Math. Anal. Appl. 360:1 (2009), 307-316 The source file(s), balashov+repovs2-final.tex: 49005 bytes, is(are) stored in gzipped form as 0908.1216.gz with size 15kb. The corresponding postcript file has gzipped size 91kb. Submitted from: dusan.repovs(a)guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1216 or http://arXiv.org/abs/0908.1216 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1216 or in gzipped form by using subject line get 0908.1216 to: math(a)arXiv.org.

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New email address for M Ledoux
by Dale Alspach 03 Sep '09

03 Sep '09

Dear colleagues, please note my new email address ledoux(a)math.univ-toulouse.fr Sincerely yours. M. Ledoux

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