Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Ilijas Farah and Saharon Shelah
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "A dichotomy for the number of ultrapowers" by Ilijas Farah and Saharon Shelah. Abstract: We prove a strong dichotomy for the number of ultrapowers of a given countable model associated with nonprincipal ultrafilters on N. They are either all isomorphic, or else there are $2^{2^{\aleph_0}}$ many nonisomorphic ultrapowers. We prove the analogous result for metric structures, including C*-algebras and II$_1$ factors, as well as their relative commutants and include several applications. We also show that the C*-algebra B(H) always has nonisomorphic relative commutants in its ultrapowers associated with nonprincipal ultrafilters on N. Archive classification: math.LO math.OA Mathematics Subject Classification: 03C20, 46M07 Report Number: Shelah [FaSh:954] The source file(s), 2009i19-ultrapowers.tex: 122804 bytes, is(are) stored in gzipped form as 0912.0406.gz with size 33kb. The corresponding postcript file has gzipped size 176kb. Submitted from: ifarah(a)yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.0406 or http://arXiv.org/abs/0912.0406 or by email in unzipped form by transmitting an empty message with subject line uget 0912.0406 or in gzipped form by using subject line get 0912.0406 to: math(a)arXiv.org.

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Abstract of a paper by Alon Ivtsan
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Stafney's lemma holds for several "classical" interpolation methods" by Alon Ivtsan. Abstract: Let (B_0,B_1) be a Banach pair. Stafney showed that in the definition of the norm in the Calderon complex interpolation method on the strip, one can replace the space F(B_0,B_1) with its subspace G(B_0,B_1) if the element belongs to the intersection of B_0 and B_1. We extend this result to a more general setting, which contains several well-known interpolation methods, namely the Calderon complex interpolation method on the annulus, an appropriate version of the Lions-Peetre real method, and the Peetre "plus minus" method. Archive classification: math.FA Mathematics Subject Classification: 46B70 (primary); 46B45 (secondary) Remarks: 7 pages The source file(s), stafney30-t.tex: 35607 bytes, is(are) stored in gzipped form as 0911.5719.gz with size 9kb. The corresponding postcript file has gzipped size 84kb. Submitted from: aloniv(a)tx.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5719 or http://arXiv.org/abs/0911.5719 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5719 or in gzipped form by using subject line get 0911.5719 to: math(a)arXiv.org.

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Abstract of a paper by W. Lawton
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Minimal sequences and the Kadison-Singer problem" by W. Lawton. Abstract: The Kadison-Singer problem asks: does every pure state on the C$^*$-algebra $\ell^{\infty}(Z)$ admit a unique extension to the C$^*$-algebra $\cB(\ell^2(Z))$? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We prove that for measurable $S \subset \TT,$ $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k\in \ZZ}}$ is a finite union of Riesz sequences in $L^2(\TT)$ if and only if there exists a nonempty $\Lambda \subset \ZZ$ such that $\chi_{_\Lambda}$ is a minimal sequence and $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k \in \Lambda}}$ is a Riesz sequence. We also suggest some directions for future research. Archive classification: math.FA math.DS Mathematics Subject Classification: 37B10, 42A55, 46L05 Remarks: 10 pages, Theorem 1.1 was announced during conferences in St. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5559 or http://arXiv.org/abs/0911.5559 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5559 or in gzipped form by using subject line get 0911.5559 to: math(a)arXiv.org.

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Abstract of a paper by Rafa Espinola and Aurora Fernandez-Leon
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "On best proximity points in metric and Banach spaces" by Rafa Espinola and Aurora Fernandez-Leon. Abstract: In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We do it from two different approaches, leading each one of them to different results which complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with. Archive classification: math.FA math.MG Mathematics Subject Classification: 54H25, 47H09 Remarks: 17 pages. Accepted for publication in the Canadian Mathematical The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5263 or http://arXiv.org/abs/0911.5263 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5263 or in gzipped form by using subject line get 0911.5263 to: math(a)arXiv.org.

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conference in Cleveland
by Elisabeth Werner 17 Dec '09

17 Dec '09

CONFERENCE ON "PERSPECTIVES IN HIGH DIMENSIONS," CLEVELAND, AUGUST 1-7, 2010 This is an announcement of the conference on "Perspectives in High Dimensions," to be held on the campus of Case Western Reserve University in Cleveland, Ohio, U.S.A. from August 1 until August 7, 2010. The aim of the conference is to reflect on recent and future developments in broadly understood geometric functional analysis, with emphasis on interactions with other subfields of mathematics and with other mathematical sciences, including but not limited to computer science, mathematical physics and statistics. The scientific program will be set up under the guidance of the Scientific Committee consisting of Jean Bourgain Emmanuel Candes Persi Diaconis Boaz Klartag Stanislaw Szarek Santosh Vempala Roman Vershynin Elisabeth Werner The conference will be supported by the NSF via Focused Research Grant, which involves CWRU, Kent State University, University of Michigan and University of Missouri. We expect to be able to provide support to a substantial number of participants, with priority given to graduate students, junior researchers and to those lacking their own research funding, as well as to members of underrepresented groups. More details will be provided in the coming months. Should you have any questions, please contact one of the organizers (below), or check the temporary conference website at http://www.case.edu/artsci/math/perspectivesInHighDimensions/ Alexander Koldobsky (koldobskiya at missouri.edu) Mark Rudelson (rudelsonm at missouri.edu) Dmitry Ryabogin (ryabogin at math.kent.edu) Stanislaw Szarek (szarek at cwru.edu) Roman Vershynin (romanv at umich.edu) Elisabeth Werner (elisabeth.werner at case.edu) Artem Zvavitch (zvavitch at math.kent.edu) Local committee: Elizabeth Meckes (ese3 at cwru.edu) Mark Meckes (mark.meckes at case.edu) Dmitry Ryabogin (ryabogin at math.kent.edu) Stanislaw Szarek (szarek at cwru.edu) Elisabeth Werner (elisabeth.werner at case.edu) Artem Zvavitch (zvavitch at math.kent.edu)

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Abstract of a paper by Daniel A. Spielman and Nikhil Srivastava
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "An elementary proof of the Restricted Invertibility Theorem" by Daniel A. Spielman and Nikhil Srivastava. Abstract: We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace. Archive classification: math.FA The source file(s), restrict.tex: 13698 bytes, is(are) stored in gzipped form as 0911.1114.gz with size 5kb. The corresponding postcript file has gzipped size 58kb. Submitted from: nikhil.srivastava(a)yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.1114 or http://arXiv.org/abs/0911.1114 or by email in unzipped form by transmitting an empty message with subject line uget 0911.1114 or in gzipped form by using subject line get 0911.1114 to: math(a)arXiv.org.

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Abstract of a paper by Elisabeth M. Werner and Deping Ye
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "On the Homothety Conjecture" by Elisabeth M. Werner and Deping Ye. Abstract: Let $K$ be a convex body in $\bbR^n$ and $\d>0$. The homothety conjecture asks: Does $K_{\d}=c K$ imply that $K$ is an ellipsoid? Here $K_{\d}$ is the (convex) floating body and $c$ is a constant depending on $\d$ only. In this paper we prove that the homothety conjecture holds true in the class of the convex bodies $B^n_p$, $1\leq p\leq \infty$, the unit balls of $l_p^n$; namely, we show that $(B^n_p)_{\d} = c B^n_p$ if and only if $p=2$. We also show that the homothety conjecture is true for a general convex body $K$ if $\d$ is small enough. This improvs earlier results by Sch\"utt and Werner \cite{SW1994} and Stancu \cite{Stancu2009}. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Remarks: 24 pages, 2 figures The source file(s), floating-2.jpg: 38222 bytes floating.jpg: 27480 bytes homothety102609.tex: 58622 bytes, is(are) stored in gzipped form as 0911.0642.tar.gz with size 68kb. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0642 or http://arXiv.org/abs/0911.0642 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0642 or in gzipped form by using subject line get 0911.0642 to: math(a)arXiv.org.

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Abstract of a paper by Roman Vershynin
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Approximating the moments of marginals of high dimensional distributions" by Roman Vershynin. Abstract: For probability distributions on R^n, we study the optimal sample size N=N(n,p) that suffices to uniformly approximate the p-th moments of all one-dimensional marginals. Under the assumption that the support of the distribution lies in the Euclidean ball of radius \sqrt{n} and the marginals have bounded 4p moments, we obtain the optimal bound N = O(n^{p/2}) for p > 2. This bound goes in the direction of bridging the two recent results: a theorem of Guedon and Rudelson which has an extra logarithmic factor in the sample size, and a recent result of Adamczak, Litvak, Pajor and Tomczak-Jaegermann which requires stronger subexponential moment assumptions. Archive classification: math.PR math.FA Mathematics Subject Classification: 46B09; 52A21; 62J10 Remarks: 12 pages The source file(s), moments-of-marginals.tex: 32410 bytes, is(are) stored in gzipped form as 0911.0391.gz with size 11kb. The corresponding postcript file has gzipped size 92kb. Submitted from: romanv(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0391 or http://arXiv.org/abs/0911.0391 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0391 or in gzipped form by using subject line get 0911.0391 to: math(a)arXiv.org.

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Abstract of a paper by A. J. Scott and M. Grassl
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "SIC-POVMs: A new computer study" by A. J. Scott and M. Grassl. Abstract: We report on a new computer study into the existence of d^2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the underlying mathematical objects defining symmetric informationally complete measurements in quantum theory. We provide numerical solutions in all dimensions d <= 67 and, moreover, a putatively complete list of Weyl-Heisenberg covariant solutions for d <= 50. A symmetry analysis of this list leads to new algebraic solutions in dimensions d = 24, 35 and 48, which are given together with algebraic solutions for d = 4,..., 15 and 19. Archive classification: quant-ph math.CO math.FA Remarks: 20 pages + 189 pages of raw data (also accessible in the source in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.5784 or http://arXiv.org/abs/0910.5784 or by email in unzipped form by transmitting an empty message with subject line uget 0910.5784 or in gzipped form by using subject line get 0910.5784 to: math(a)arXiv.org.

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Abstract of a paper by Roland Speicher
by alspach＠fourier.math.okstate.edu 12 Nov '09

12 Nov '09

This is an announcement for the paper "Free probability theory" by Roland Speicher. Abstract: Free probability theory was created by Dan Voiculescu around 1985, motivated by his efforts to understand special classes of von Neumann algebras. His discovery in 1991 that also random matrices satisfy asymptotically the freeness relation transformed the theory dramatically. Not only did this yield spectacular results about the structure of operator algebras, but it also brought new concepts and tools into the realm of random matrix theory. In the following we will give, mostly from the random matrix point of view, a survey on some of the basic ideas and results of free probability theory. Archive classification: math.PR math.OA Remarks: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press The source file(s), RMT-chapter22.tex: 56575 bytes wignerpluswishart.ps: 11793 bytes wisharttimeswishart.ps: 10691 bytes, is(are) stored in gzipped form as 0911.0087.tar.gz with size 23kb. The corresponding postcript file has gzipped size 119kb. Submitted from: speicher(a)mast.queensu.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.0087 or http://arXiv.org/abs/0911.0087 or by email in unzipped form by transmitting an empty message with subject line uget 0911.0087 or in gzipped form by using subject line get 0911.0087 to: math(a)arXiv.org.

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