Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Gilles Pisier
by Dale Alspach 26 Aug '05

26 Aug '05

This is an announcement for the paper "Simultaneous similarity, bounded generation and amenability" by Gilles Pisier. Abstract: We prove that a discrete group $G$ is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation $\pi$ on $G$ can be unitarized by an invertible chosen in the von Neumann algebra generated by the range of $\pi$. Analogously a $C^*$-algebra $A$ is nuclear iff any bounded homomorphism $u:\ A\to B(H)$ is strongly similar to a $*$-homomorphism in the sense that there is an invertible operator $\xi$ in the von Neumann algebra generated by the range of $u$ such that $a\to \xi u(a) \xi^{-1}$ is a $*$-homomorphism. An analogous characterization holds in terms of derivations. We apply this to answer several questions left open in our previous work concerning the length $\ell(A,B)$ of the maximal tensor product $A\otimes_{\max} B$ of two unital $C^*$-algebras, when we consider its generation by the subalgebras $A\otimes 1$ and $1\otimes B$. We show that if $\ell(A,B)<\infty$ either for $B=B(\ell_2)$ or when $B$ is the $C^*$-algebra (either full or reduced) of a non Abelian free group, then $A$ must be nuclear. We also show that $\ell(A,B)\le d$ iff the canonical quotient map from the unital free product $A\ast B$ onto $A\otimes_{\max} B$ remains a complete quotient map when restricted to the closed span of the words of length $\le d$. Archive classification: Operator Algebras; Functional Analysis Mathematics Subject Classification: Primary 46 L06. Secondary: 46L07, 46L57 Primary 46 L06. Secondary: The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0508223 or http://arXiv.org/abs/math.OA/0508223 or by email in unzipped form by transmitting an empty message with subject line uget 0508223 or in gzipped form by using subject line get 0508223 to: math(a)arXiv.org.

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Abstract of a paper by Anna Maria Pelczar
by Dale Alspach 26 Aug '05

26 Aug '05

This is an announcement for the paper "Stabilization of Tsirelson-type norms on $\ell_p$ spaces" by Anna Maria Pelczar. Abstract: We consider classical Tsirelson-type norms of $T[A_r,\theta]$ and their modified versions on $\ell_p$ spaces. We show that for any $1<p<\infty$ there is a constant $\lambda_p$ such that considered Tsirelson-type norms do not $\lambda_p$-distort any of subspaces of $\ell_p$. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03 Remarks: 10 pages The source file(s), stab-tsir.tex: 27412 bytes, is(are) stored in gzipped form as 0508352.gz with size 9kb. The corresponding postcript file has gzipped size 57kb. 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/math.FA/0508352 or http://arXiv.org/abs/math.FA/0508352 or by email in unzipped form by transmitting an empty message with subject line uget 0508352 or in gzipped form by using subject line get 0508352 to: math(a)arXiv.org.

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Abstract of a paper by Javier Parcet
by Dale Alspach 26 Aug '05

26 Aug '05

This is an announcement for the paper "Weak type estimates associated to Burkholder's martingale inequality" by Javier Parcet. Abstract: Given a probability space $(\Omega, \mathsf{A}, \mu)$, let $\mathsf{A}_1, \mathsf{A}_2, \ldots$ be a filtration of $\sigma$-subalgebras of $\mathsf{A}$ and let $\mathsf{E}_1, \mathsf{E}_2, \ldots$ denote the corresponding family of conditional expectations. Given a martingale $f = (f_1, f_2, \ldots)$ adapted to this filtration and bounded in $L_p(\Omega)$ for some $2 \le p < \infty$, Burkholder's inequality claims that $$\|f\|_{L_p(\Omega)} \sim_{\mathrm{c}_p} \Big\| \Big( \sum_{k=1}^\infty \mathsf{E}_{k-1}(|df_k|^2) \Big)^{1/2} \Big\|_{L_{p}(\Omega)} + \Big( \sum_{k=1}^\infty \|df_k\|_p^p \Big)^{1/p}.$$ Motivated by quantum probability, Junge and Xu recently extended this result to the range $1 < p < 2$. In this paper we study Burkholder's inequality for $p=1$, for which the techniques (as we shall explain) must be different. Quite surprisingly, we obtain two non-equivalent estimates which play the role of the weak type $(1,1)$ analog of Burkholder's inequality. As application, we obtain new properties of Davis decomposition for martingales. Archive classification: Probability; Functional Analysis Mathematics Subject Classification: 42B25; 60G46; 60G50 Remarks: 19 pages The source file(s), WeakBurk.tex: 66319 bytes, is(are) stored in gzipped form as 0508447.gz with size 18kb. The corresponding postcript file has gzipped size 88kb. Submitted from: javier.parcet(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.PR/0508447 or http://arXiv.org/abs/math.PR/0508447 or by email in unzipped form by transmitting an empty message with subject line uget 0508447 or in gzipped form by using subject line get 0508447 to: math(a)arXiv.org.

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Abstract of a paper by Marc A. Rieffel
by Dale Alspach 08 Aug '05

08 Aug '05

This is an announcement for the paper "Lipschitz extension constants equal projection constants" by Marc A. Rieffel. Abstract: For a finite-dimensional Banach space $V$ we define its Lipschitz extension constant, $\cL\cE(V)$, to be the smallest constant $c$ such that for every compact metric space $(Z,\rho)$, every $X \subset Z$, and every $f: X \to V$, there is an extension, $g$, of $f$ to $Z$ such that $L(g) \le cL(f)$, where $L$ denotes the Lipschitz constant. Our main theorem is that $\cL\cE(V) = \cP\cC(V)$ where $\cP\cC(V)$ is the well-known projection constant of $V$. We obtain some consequences, especially when $V = M_n(\bC)$. We also discuss what happens if we also require that $\|g\|_{\infty} = \|f\|_{\infty}$. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 46B20; 26A16 Remarks: 12 pages. Intended for the proceedings of GPOTS05 The source file(s), liparc.tex: 35141 bytes, is(are) stored in gzipped form as 0508097.gz with size 12kb. The corresponding postcript file has gzipped size 61kb. Submitted from: rieffel(a)math.berkeley.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508097 or http://arXiv.org/abs/math.FA/0508097 or by email in unzipped form by transmitting an empty message with subject line uget 0508097 or in gzipped form by using subject line get 0508097 to: math(a)arXiv.org.

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Abstract of a paper by M. Junge, D. Kutzarova and E. Odell
by Dale Alspach 02 Aug '05

02 Aug '05

This is an announcement for the paper "On asymptotically symmetric Banach spaces" by M. Junge, D. Kutzarova and E. Odell. Abstract: We define and study asymptotically symmetric Banach spaces (a.s.) and its variations: weakly a.s. (w.a.s.) and weakly normalized a.s. (w.n.a.s.). If X is a.s. then all spreading models of X are uniformly symmetric. We show that the converse fails. We also show that w.a.s. and w.n.a.s. are not equivalent properties and that Schlumprecht's space S fails to be w.n.a.s. We show that if X is separable and has the property that every normalized weakly null sequence in X has a subsequence equivalent to the unit vector basis of c_0 then X is w.a.s.. We obtain an analogous result if c_0 is replaced by ell_1 and also show it is false if c_0 is replaced by ell_p, 1 < p < infinity. We prove that if 1 less than or equal p < infinity and the norm of the sum of (x_i)_1^n is of the order n^{1/p} for all (x_i)_1^n in the n^{th} asymptotic structure of $X$, then X contains an asymptotic ell_p, hence w.a.s. subspace. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; 46B20 Remarks: 22 pages, AMSLaTeX The source file(s), jko31.tex: 68725 bytes, is(are) stored in gzipped form as 0508035.gz with size 21kb. The corresponding postcript file has gzipped size 107kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508035 or http://arXiv.org/abs/math.FA/0508035 or by email in unzipped form by transmitting an empty message with subject line uget 0508035 or in gzipped form by using subject line get 0508035 to: math(a)arXiv.org.

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conference at U of Missouri.
by Dale Alspach 01 Aug '05

01 Aug '05

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% SECOND ANNOUNCEMENT Seminar on Analysis December 9-10, 2005 in honor of Elias Saab's 60th birthday. The following have accepted to give talks in this meeting: Joe Diestel (Kent State) Gilles Godefroy (University of Paris VI) Steve Hofmann (MU) Alex Koldobsky (MU) Marius Mitrea (MU) Narcisse Randrianantoanina (Miami University, OH) Mark Rudelson (MU) Jerry Uhl (Urbana-Champaign) For more up to date information on this conference please visit http://www.math.missouri.edu/~organizers/ Partial support is available for graduate students and recent Ph.D. recipients. Women and minorities are particularly encouraged to apply. For instructions on how to apply go to http://www.math.missouri.edu/~organizers/financial.htm If you have any questions please contact the organizers by e-mail at organizers(a)math.missouri.edu The Seminar on Analysis is sponsored by the University of Missouri-Columbia College of Arts and Science and the Department of Mathematics. The organizers, Fritz Gesztesy and Dorina Mitrea %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -- %------------------------------------------- % Dorina Mitrea | % University of Missouri-Columbia | % Department of Mathematics | % 202 Math Sciences Bldg | % Columbia, MO 65211 | % | % Phone: (573)-882-4233 | % Fax: (573)-882-1869 | % e-mail: dorina(a)math.missouri.edu | % http://www.math.missouri.edu/ | %--------------------------------------------

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Abstract of a paper by E. Odell and Th. Schlumprecht
by Dale Alspach 26 Jul '05

26 Jul '05

This is an announcement for the paper "A universal reflexive space for the class of uniformly convex Banach spaces" by E. Odell and Th. Schlumprecht. Abstract: We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J.~Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian finite dimensional decomposition. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; secondary 46B20 Remarks: 13 pages, amslatex The source file(s), os-universal2-archive.tex: 45823 bytes, is(are) stored in gzipped form as 0507509.gz with size 14kb. The corresponding postcript file has gzipped size 78kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507509 or http://arXiv.org/abs/math.FA/0507509 or by email in unzipped form by transmitting an empty message with subject line uget 0507509 or in gzipped form by using subject line get 0507509 to: math(a)arXiv.org.

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Pictures of Haskell Rosenthal
by Dale Alspach 20 Jul '05

20 Jul '05

Haskell Rosenthal retired from The University of Texas this past fall after a long and distinguished career. Haskell's wife, Gayle Rosenthal, would like to receive copies of any photos or e-photos or discs, anything with photos of Haskell, lecturing, hiking, dancing, drinking, or anything else, including photos of friends or places he's known or been to. She is preparing a video montage to be shown during Haskellfest at Texas A&M University, August 4-5, 2005. e-Photos should be sent to: Gayle Rosenthal <gayle-rosenthal(a)austin.rr.com> Hard copies of photos should be sent to: Gayle Rosenthal 311 Nixon Drive Austin TX 78746

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Abstract of a paper by Hermann Pfitzner
by Dale Alspach 19 Jul '05

19 Jul '05

This is an announcement for the paper "A separable L-embedded Banach space has property (X) and is therefore the unique predual of its dual" by Hermann Pfitzner. Abstract: In this note the following is proved. Separable L-embedded spaces - that is separable Banach spaces which are complemented in their biduals such that the norm between the two complementary subspaces is additive - have property (X) which, by a result of Godefroy and Talagrand, entails uniqueness of the space as a predual. Archive classification: Functional Analysis Mathematics Subject Classification: 46B04, 46B03, 46B20 The source file(s), Property_X.tex: 22448 bytes, is(are) stored in gzipped form as 0507354.gz with size 8kb. The corresponding postcript file has gzipped size 41kb. Submitted from: Hermann.Pfitzner(a)univ-orleans.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507354 or http://arXiv.org/abs/math.FA/0507354 or by email in unzipped form by transmitting an empty message with subject line uget 0507354 or in gzipped form by using subject line get 0507354 to: math(a)arXiv.org.

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Abstract of a paper by Mark Rudelson
by Dale Alspach 04 Jul '05

04 Jul '05

This is an announcement for the paper "Invertibility of random matrices: norm of the inverse" by Mark Rudelson. Abstract: Let A be an n by n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} does not exceed Cn^{3/2} with probability close to 1. Archive classification: Functional Analysis Mathematics Subject Classification: 15A52, 46B09 Remarks: 25 pages The source file(s), square-matrix.tex: 58844 bytes, is(are) stored in gzipped form as 0507024.gz with size 18kb. The corresponding postcript file has gzipped size 94kb. Submitted from: rudelson(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507024 or http://arXiv.org/abs/math.FA/0507024 or by email in unzipped form by transmitting an empty message with subject line uget 0507024 or in gzipped form by using subject line get 0507024 to: math(a)arXiv.org.

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