Banach February 2004

banach@mathdept.okstate.edu

2 participants
12 discussions

Abstract of a paper by Javier Parcet and Gilles Pisier
by Dale Alspach 20 Feb '04

20 Feb '04

This is an announcement for the paper "Non-commutative Khintchine type inequalities associated with free groups" by Javier Parcet and Gilles Pisier. Abstract: Let Fn denote the free group with n generators g1,g2,..,gn. Let $\lambda$ stand for the left regular representation of Fn and let $\tau$ be the standard trace associated to $\lambda$. Given any positive integer d, we study the operator space structure of the subspace Wp(n,d) of Lp(\tau) generated by the family of operators $\lambda(g_{i_1}g_{i_2} ... g_{i_d})$ with $1 \le i_k \le n$. Moreover, our description of this operator space holds up to a constant which does not depend on n or p, so that our result remains valid for infinitely many generators. We also consider the subspace of L_p(\tau) generated by the image under $\lambda$ of the set of reduced words of length d. Our result extends to any exponent $1 \le p \le \infty$ a previous result of Buchholz for the space $W_{\infty}(n,d)$. Archive classification: Operator Algebras; Functional Analysis Mathematics Subject Classification: 46L52; 46L53 Remarks: 19 pages The source file(s), Free.tex: 71069 bytes, is(are) stored in gzipped form as 0312300.gz with size 17kb. The corresponding postcript file has gzipped size 94kb. 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.OA/0312300 or http://arXiv.org/abs/math.OA/0312300 or by email in unzipped form by transmitting an empty message with subject line uget 0312300 or in gzipped form by using subject line get 0312300 to: math(a)arXiv.org.

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Abstract of a paper by Jaroslaw Wawrzycki
by Dale Alspach 18 Feb '04

18 Feb '04

This is an announcement for the paper "A generalization of the Markov-Kakutani fixed point theorem" by Jaroslaw Wawrzycki. Abstract: In this announcement we generalize the Markov-Kakutani fixed point theorem for abelian semi-groups of affine transformations extending it on some class of non-commutative semi-groups. As an interesting example we apply it obtaining a generalization of the invariant version of the Hahn-Banach theorem. Archive classification: Functional Analysis Mathematics Subject Classification: 46A22, 46A55 Remarks: 5 pages, Latex preparation The source file(s), kakutani.tex: 11176 bytes, is(are) stored in gzipped form as 0402255.gz with size 4kb. The corresponding postcript file has gzipped size 32kb. Submitted from: Jaroslaw.Wawrzycki(a)ifj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0402255 or http://arXiv.org/abs/math.FA/0402255 or by email in unzipped form by transmitting an empty message with subject line uget 0402255 or in gzipped form by using subject line get 0402255 to: math(a)arXiv.org.

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Abstract of a paper by I. Gasparis, E. Odell, and B. Wahl
by Dale Alspach 13 Feb '04

13 Feb '04

This is an announcement for the paper "Weakly null sequences in the Banach space C(K)" by I. Gasparis, E. Odell, and B. Wahl. Abstract: The hierarchy of the block bases of transfinite normalized averages of a normalized Schauder basic sequence is introduced and a criterion is given for a normalized weakly null sequence in C(K), the Banach space of scalar valued functions continuous on the compact metric space K, to admit a block basis of normalized averages equivalent to the unit vector basis of c_0, the Banach space of null scalar sequences. As an application of this criterion, it is shown that every normalized weakly null sequence in C(K), for countable K, admits a block basis of normalized averages equivalent to the unit vector basis of c_0. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03 Remarks: 36 pages The source file(s), gow5.tex: 137843 bytes, is(are) stored in gzipped form as 0402202.gz with size 33kb. The corresponding postcript file has gzipped size 147kb. 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/0402202 or http://arXiv.org/abs/math.FA/0402202 or by email in unzipped form by transmitting an empty message with subject line uget 0402202 or in gzipped form by using subject line get 0402202 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge, Zhong-Jin Ruan and David Sherman
by Dale Alspach 12 Feb '04

12 Feb '04

This is an announcement for the paper "A classification for 2-isometries of noncommutative Lp-spaces" by Marius Junge, Zhong-Jin Ruan and David Sherman. Abstract: In this paper we extend previous results of Banach, Lamperti and Yeadon on isometries of Lp-spaces to the non-tracial case first introduced by Haagerup. Specifically, we use operator space techniques and an extrapolation argument to prove that every 2-isometry T : Lp(M) to Lp(N) between arbitrary noncommutative Lp-spaces can always be written in the form T(phi^{1/p}) = w (phi circ pi^{-1} circ E)^{1/p}, for phi in M_*^+. Here pi is a normal *-isomorphism from M onto the von Neumann subalgebra pi(M) of N, w is a partial isometry in N, and E is a normal conditional expectation from N onto pi(M). As a consequence of this, any 2-isometry is automatically a complete isometry and has completely contractively complemented range. Archive classification: Operator Algebras Remarks: 25 pages The source file(s), 2isom.tex: 88005 bytes, is(are) stored in gzipped form as 0402181.gz with size 26kb. The corresponding postcript file has gzipped size 111kb. Submitted from: dasherma(a)ux1.cso.uiuc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0402181 or http://arXiv.org/abs/math.OA/0402181 or by email in unzipped form by transmitting an empty message with subject line uget 0402181 or in gzipped form by using subject line get 0402181 to: math(a)arXiv.org.

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Functional Analysis Workshop in Finland
by Dale Alspach 11 Feb '04

11 Feb '04

FUNCTIONAL ANALYSIS WORKSHOP JOENSUU, FINLAND June 20.-24., 2004 The workshop is a satellite conference of the 4th European Congress of Mathematics (4ecm) in Stockholm. The topics of this workshop include Banach spaces and operator theory, Frechet and related spaces, and applications to analytic function spaces. There will be 13 invited plenary lectures and, in addition, shorter talks by the participants. Main plenary lectures will be given by: Klaus Bierstedt (Paderborn) Jose Bonet (Valencia) Alexander Borichev (Bordeaux) Gilles Godefroy (Paris) Chen Huaihui (Nanjing) Serguei Kislyakov (St. Petersburg) Reinhold Meise (Dusseldorf) Artur Nicolau (Barcelona) Edward Odell (Austin) David Preiss (London) Eero Saksman (Jyvaskyla) Joel Shapiro (East Lansing) Dietmar Vogt (Wuppertal) Scientific committee: Jari Taskinen (Joensuu, chair), Rauno Aulaskari (Joensuu), Mikael Lindstr\"om (Abo), Hans-Olav Tylli (Helsinki). Joensuu is a pleasant mid-size town in eastern Finland, which is conveniently accessible from Helsinki by frequent trains or flights. The scientific programme of the workshop will commence on the morning of June 21. More information about the workshop (registration, programme, accommodation, contact addresses, location) can be found on the www-page http://www.joensuu.fi/mathematics/workshop2004

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Abstract of a paper by Joram Lindenstrauss and David Preiss
by Dale Alspach 11 Feb '04

11 Feb '04

This is an announcement for the paper "On Fr\'echet differentiability of Lipschitz maps between Banach spaces" by Joram Lindenstrauss and David Preiss. Abstract: A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Frechet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality). Our aims are achieved by introducing a new class of null sets in Banach spaces (called $\Gamma$-null sets), whose definition involves both the notions of category and measure, and showing that the required differentiability holds almost everywhere with respect to it. We even obtain existence of Fr\'echet derivatives of Lipschitz functions between certain infinite-dimensional Banach spaces;no such results have been known previously. Our main result states that a Lipschitz map between separable Banach spaces is Fr\'echet differentiable $\Gamma$-almost everywhere provided that it is regularly Gateaux differentiable $\Gamma$-almost everywhere and the Gateaux derivatives stay within a norm separable space of operators. It is easy to see that Lipschitz maps of X to spaces with the Radon-Nikodym property are Gateaux differentiable $\Gamma$-almost everywhere. Moreover, Gateaux differentiability implies regular Gateaux differentiability with exception of another kind of negligible sets, so-called $\sigma$-porous sets. The answer to the question is therefore positive in every space in which every $\sigma$-porous set is $\Gamma$-null. We show that this holds for $C(K)$ with $K$ countable compact, the Tsirelson space and for all subspaces of $c_0$, but that it fails for Hilbert spaces. Archive classification: Functional Analysis Citation: Ann. of Math. (2), Vol. 157 (2003), no. 1, 257--288 Remarks: 32 pages, published version The source file(s), amlts.sty: 33990 bytes, lindenstrauss.tex: 89631 bytes, is(are) stored in gzipped form as 0402160.tar.gz with size 36kb. The corresponding postcript file has gzipped size 100kb. Submitted from: dp(a)math.ucl.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0402160 or http://arXiv.org/abs/math.FA/0402160 or by email in unzipped form by transmitting an empty message with subject line uget 0402160 or in gzipped form by using subject line get 0402160 to: math(a)arXiv.org.

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Abstract of a paper by E.Ournycheva and B.Rubin
by Dale Alspach 10 Feb '04

10 Feb '04

This is an announcement for the paper "An analogue of the Fuglede formula in integral geometry on matrix spaces" by E.Ournycheva and B.Rubin. Abstract: The well known formula of B. Fuglede expresses the mean value of the Radon k-plane transform on $R^n$ as a Riesz potential. We extend this formula to the space of $n \times m$ real matrices and show that the corresponding matrix k-plane transform $f \to \hat f$ is injective if and only if $n-k \ge m$. Different inversion formulas for this transform are obtained. We assume that $f \in L^p$ or $f$ is a continuous function satisfying certain "minimal" conditions at infinity. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 44A12; Secondary 47G10 Remarks: AMS LaTeX, 20 pages The source file(s), Fug8.tex: 50342 bytes, is(are) stored in gzipped form as 0401127.gz with size 18kb. The corresponding postcript file has gzipped size 82kb. Submitted from: ournyce(a)math.huji.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0401127 or http://arXiv.org/abs/math.FA/0401127 or by email in unzipped form by transmitting an empty message with subject line uget 0401127 or in gzipped form by using subject line get 0401127 to: math(a)arXiv.org.

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Abstract of a paper by Omran Kouba
by Dale Alspach 10 Feb '04

10 Feb '04

This is an announcement for the paper "On the interpolation of injective or projective tensor products of Banach spaces" by Omran Kouba. Abstract: We prove a general result on the factorization of matrix-valued analytic functions. We deduce that if $(E_0,E_1)$ and $(F_0,F_1)$ are interpolation pairs with dense intersections, then under some conditions on the spaces $E_0$, $E_1$, $F_0$ and $F_1$, we have $$ [E_0\hat\otimes F_0,E_1\hat\otimes F_1]_t= [E_0 ,E_1]_t\hat\otimes[F_0 ,F_1]_t, 0 < t< 1.$$ We find also conditions on the spaces $E_0$, $E_1$, $F_0$ and $F_1$, so that the following holds $$ [E_0\wcheck\otimes F_0,E_1\wcheck\otimes F_1]_t= [E_0,E_1]_t\wcheck\otimes [F_0,F_1]_t, 0 <t< 1.$$ Some applications of these results are also considered. Archive classification: Functional Analysis Mathematics Subject Classification: 46B70;47A56;47A68;46M05;46B07 Citation: J. Funct. Anal. 96 (1991), 38-61 Remarks: 26 pages The source file(s), ART3.Tex: 75244 bytes, is(are) stored in gzipped form as 0401337.gz with size 22kb. The corresponding postcript file has gzipped size 93kb. Submitted from: omran_kouba(a)hiast.edu.sy The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0401337 or http://arXiv.org/abs/math.FA/0401337 or by email in unzipped form by transmitting an empty message with subject line uget 0401337 or in gzipped form by using subject line get 0401337 to: math(a)arXiv.org.

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Abstract of a paper by Omran Kouba
by Dale Alspach 10 Feb '04

10 Feb '04

This is an announcement for the paper "L'Application canonique $J:H^2(X) \otimes H^2(X)->H^1(X\otimes X)$ n'est pas surjective en g\'en\'eral" by Omran Kouba. Abstract: We introduce the $H^1$-projective property, and use it to construct a Banach space $X$ such that the natural map $J:H^2(X)\otimes H^2(X) -> H^1(X\otimes X)$ is not onto. Archive classification: Functional Analysis Mathematics Subject Classification: 46M05;47A56;47A68 Citation: C.R. Acad. Sci. Paris t.307, Serie I, (1988), 949-953 Remarks: 9 pages, French with abridged english version The source file(s), ART1.Tex: 27483 bytes, is(are) stored in gzipped form as 0401335.gz with size 9kb. The corresponding postcript file has gzipped size 45kb. Submitted from: omran_kouba(a)hiast.edu.sy The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0401335 or http://arXiv.org/abs/math.FA/0401335 or by email in unzipped form by transmitting an empty message with subject line uget 0401335 or in gzipped form by using subject line get 0401335 to: math(a)arXiv.org.

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Abstract of a paper by B. Klartag
by Dale Alspach 10 Feb '04

10 Feb '04

This is an announcement for the paper "An isomorphic version of the slicing problem" by B. Klartag. Abstract: Here we show that any n-dimensional centrally symmetric convex body K has an n-dimensional perturbation T which is convex and centrally symmetric, such that the isotropic constant of T is universally bounded. T is close to K in the sense that the Banach-Mazur distance between T and K is O(log n). If K has a non-trivial type then the distance is universally bounded. In addition, if K is quasi-convex then there exists a quasi-convex T with a universally bounded isotropic constant and with a universally bounded distance to K. Archive classification: Metric Geometry; Functional Analysis Remarks: 19 pages The source file(s), mixed_MM_star.tex: 44341 bytes, is(are) stored in gzipped form as 0312475.gz with size 13kb. The corresponding postcript file has gzipped size 72kb. Submitted from: klartagb(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0312475 or http://arXiv.org/abs/math.MG/0312475 or by email in unzipped form by transmitting an empty message with subject line uget 0312475 or in gzipped form by using subject line get 0312475 to: math(a)arXiv.org.

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Banach February 2004