August 2009 - Banach - mathdept.okstate.edu

Abstract of a paper by Kevin Beanland
by Dale Alspach 17 Aug '09

17 Aug '09

This is an announcement for the paper "Operators on asymptotic $\ell_p$ spaces which are not compact perturbations of a multiple of the identity" by Kevin Beanland. Abstract: We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of strictly singular non-compact operators on the HI spaces constructed by G. Androulakis and the author and by I. Deliyanni and A. Manoussakis. Additionally we show that under these same conditions on the space $X$, $\ell_\infty$ embeds isomorphically into the space of bounded linear operators on $X$. Archive classification: math.FA The source file(s), SSnonCPT.tex: 51728 bytes, is(are) stored in gzipped form as 0908.1107.gz with size 16kb. The corresponding postcript file has gzipped size 120kb. Submitted from: kbeanland(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.1107 or http://arXiv.org/abs/0908.1107 or by email in unzipped form by transmitting an empty message with subject line uget 0908.1107 or in gzipped form by using subject line get 0908.1107 to: math(a)arXiv.org.

1 0

Abstract of a paper by Elena Ournycheva and Boris Rubin
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "On Y. Nievergelt's inversion formula for the Radon transform" by Elena Ournycheva and Boris Rubin. Abstract: We generalize Y. Nievergelt's inversion method for the Radon transform on lines in the 2-plane to the $k$-plane Radon transform of continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$. Archive classification: math.FA Mathematics Subject Classification: Primary 42C40; Secondary 44A12 Remarks: 9 pages The source file(s), niev-amsproc4.tex: 29069 bytes, is(are) stored in gzipped form as 0908.0492.gz with size 10kb. The corresponding postcript file has gzipped size 78kb. Submitted from: elo10(a)pitt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.0492 or http://arXiv.org/abs/0908.0492 or by email in unzipped form by transmitting an empty message with subject line uget 0908.0492 or in gzipped form by using subject line get 0908.0492 to: math(a)arXiv.org.

1 0

Abstract of a paper by Stephen Simons
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Banach SSD spaces and classes of monotone sets" by Stephen Simons. Abstract: In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. We obtain some new results about these, as well as some new proofs of old ones. Archive classification: math.FA Mathematics Subject Classification: 47H05, 47N10, 46N10 The source file(s), SSDMONarxiv.tex: 116002 bytes, is(are) stored in gzipped form as 0908.0383.gz with size 29kb. The corresponding postcript file has gzipped size 133kb. Submitted from: simons(a)math.ucsb.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0908.0383 or http://arXiv.org/abs/0908.0383 or by email in unzipped form by transmitting an empty message with subject line uget 0908.0383 or in gzipped form by using subject line get 0908.0383 to: math(a)arXiv.org.

1 0

Abstract of a paper by Benoit Kloeckner
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Sharp quantitative isoperimetric inequalities in the $L^1$ Minkowski plane" by Benoit Kloeckner. Abstract: We prove that a plane domain which is almost isoperimetric (with respect to the $L^1$ metric) is close to a square whose sides are parallel to the coordinates axis. Closeness is measured either by $L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case, we determine the extremal domains. Archive classification: math.FA math.DG Mathematics Subject Classification: MSC 51M16, 51M25, 49Q20 Remarks: 9 pages The source file(s), central_square.pstex: 6034 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4945 or http://arXiv.org/abs/0907.4945 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4945 or in gzipped form by using subject line get 0907.4945 to: math(a)arXiv.org.

1 0

Abstract of a paper by Stephan Ramon Garcia and Warren R. Wogen
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "Complex symmetric partial isometries" by Stephan Ramon Garcia and Warren R. Wogen. Abstract: An operator $T \in B(\h)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T = CT^*C$. We provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B99 Citation: J. Funct. Analysis 257 (2009), 1251-1260 Remarks: 9 pages The source file(s), CSPI.tex: 33368 bytes, is(are) stored in gzipped form as 0907.4486.gz with size 10kb. The corresponding postcript file has gzipped size 68kb. Submitted from: Stephan.Garcia(a)pomona.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4486 or http://arXiv.org/abs/0907.4486 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4486 or in gzipped form by using subject line get 0907.4486 to: math(a)arXiv.org.

1 0

Abstract of a paper by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "On the hereditary proximity to $\ell_1$" by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar. Abstract: In the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to \ell_1. The second part is devoted to a complete separation of the hereditary local proximity to \ell_1 from the asymptotic one. More precisely for every countable ordinal \xi we construct a separable reflexive space \mathfrak{X}_\xi such that every infinite dimensional subspace of it has Bourgain \ell_1-index greater than \omega^\xi and the space itself has no \ell_1-spreading model. We also present a reflexive HI space admitting no \ell_p as a spreading model. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B15; 03E10; 05A17 Remarks: 40 pages, submitted for publication The source file(s), proximity.tex: 158273 bytes, is(are) stored in gzipped form as 0907.4317.gz with size 43kb. The corresponding postcript file has gzipped size 238kb. Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4317 or http://arXiv.org/abs/0907.4317 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4317 or in gzipped form by using subject line get 0907.4317 to: math(a)arXiv.org.

1 0

Abstract of a paper by Dario Cordero-Erausquin and Michel Ledoux
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "The geometry of Euclidean convolution inequalities and entropy" by Dario Cordero-Erausquin and Michel Ledoux. Abstract: The goal of this note is to show that some convolution type inequalities from Harmonic Analysis and Information Theory, such as Young's convolution inequality (with sharp constant), Nelson's hypercontractivity of the Hermite semi-group or Shannon's inequality, can be reduced to a simple geometric study of frames of $\R^2$. We shall derive directly entropic inequalities, which were recently proved to be dual to the Brascamp-Lieb convolution type inequalities. Archive classification: math.FA math.PR The source file(s), geoconv5.tex: 49291 bytes, is(are) stored in gzipped form as 0907.2861.gz with size 16kb. The corresponding postcript file has gzipped size 113kb. Submitted from: cordero(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.2861 or http://arXiv.org/abs/0907.2861 or by email in unzipped form by transmitting an empty message with subject line uget 0907.2861 or in gzipped form by using subject line get 0907.2861 to: math(a)arXiv.org.

1 0