Banach July 2004

banach@mathdept.okstate.edu

2 participants
14 discussions

Abstract of a paper by J\"org Wenzel
by Dale Alspach 29 Jul '04

29 Jul '04

This is an announcement for the paper "Strong martingale type and uniform smoothness" by J\"org Wenzel. Abstract: We introduce stronger versions of the usual notions of martingale type p <= 2 and cotype q >= 2 of a Banach space X and show that these concepts are equivalent to uniform p-smoothness and q-convexity, respectively. All these are metric concepts, so they depend on the particular norm in X. These concepts allow us to get some more insight into the fine line between X being isomorphic to a uniformly p-smooth space or being uniformly p-smooth itself. Instead of looking at Banach spaces, we consider linear operators between Banach spaces right away. The situation of a Banach space X can be rediscovered from this by considering the identity map of X. Archive classification: Functional Analysis Mathematics Subject Classification: 46B04 (Primary); 46B20, 47A63 (Secondary) Remarks: 11 pages The source file(s), strong.arxiv.tex: 30219 bytes, is(are) stored in gzipped form as 0407482.gz with size 8kb. The corresponding postcript file has gzipped size 56kb. Submitted from: wenzel(a)minet.uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407482 or http://arXiv.org/abs/math.FA/0407482 or by email in unzipped form by transmitting an empty message with subject line uget 0407482 or in gzipped form by using subject line get 0407482 to: math(a)arXiv.org.

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Abstract of a paper by J\"org Wenzel
by Dale Alspach 29 Jul '04

29 Jul '04

This is an announcement for the paper "The UMD constants of the summation operators" by J\"org Wenzel. Abstract: The UMD property of a Banach space is one of the most useful properties when one thinks about possible applications. This is in particular due to the boundedness of the vector-valued Hilbert transform for functions with values in such a space. Looking at operators instead of at spaces, it is easy to check that the summation operator does not have the UMD property. The actual asymptotic behavior however of the UMD constants computed with martingales of length n is unknown. We explain, why it would be important to know this behavior, rephrase the problem of finding these UMD constants and give some evidence of how they behave asymptotically. Archive classification: Functional Analysis Mathematics Subject Classification: 46B07 (Primary); 46B03, 46B09, 47B10 (Secondary) Remarks: 22 pages The source file(s), umd_sumop.arxiv.tex: 64167 bytes, is(are) stored in gzipped form as 0407481.gz with size 18kb. The corresponding postcript file has gzipped size 85kb. Submitted from: wenzel(a)minet.uni-jena.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407481 or http://arXiv.org/abs/math.FA/0407481 or by email in unzipped form by transmitting an empty message with subject line uget 0407481 or in gzipped form by using subject line get 0407481 to: math(a)arXiv.org.

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SUMIRFAS schedule
by Bill Johnson 29 Jul '04

29 Jul '04

Below is the tentative schedule for SUMIRFAS 2004. The final schedule will be posted on the Workshop in Linear Analysis and Probability page: http://www.math.tamu.edu/research/workshops/linanalysis/ The Home Page also contains other information about the Workshop, including a list of participants and a schedule of seminars. Housing: Contact Cheryl Williams, cherylr(a)math.tamu.edu, or Mary Chapman, mary(a)math.tamu.edu, (979/845-3621, office; 979/ 845-6028, fax) for help with housing. Please specify the type of accommodation you desire (smoking or nonsmoking), which night(s) you need the room, and roommate preference, if applicable. We expect to be able to cover housing, possibly in a double room, for most participants, from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cheryl or Mary to book your room, please let them know if you are requesting support. Rooms in CS are tight the weekend of SUMIRFAS, so please act ASAP. Dinner: There will be a dinner at 6:30 p.m. on Saturday, August 7th, at Imperial Chinese Restaurant,, 2232 S. Texas Ave. College Station. The cost for the subsidized dinner is $15 per person for faculty and $10 per person for students. Please tell Cheryl Williams or Mary Chapman, if you (and spouse or companion, if applicable) will attend. Checks should be made out to Math Dept., TAMU. ** DINNER RESERVATIONS SHOULD BE MADE BY August 2nd and PAYMENT MADE BY August 6th. ** Friday, August 6 Blocker 120 1:00-1:30 Coffee, Blocker 112 1:30-2:30 Uffe Haagerup, Random matrices and C*-algebras. 2:40-3:40 Taka Ozawa, New progress in the classification of group von Neumann algebras. 3:40-4:00 Coffee, Blocker 112 4:00-4:40 Andras Zsak, The lattice of closed ideals of a dual Banach space. 4:50-5:20 Hun Hee Lee, OH-type and OH-cotype of operator spaces and completely summing maps. Saturday, August 7 Blocker 120 9:00-9:30 Coffee & Donuts, Blocker 112 9:30-10:30 Michael Lacey, Hankel operators and product BMO. 10:40-11:40 Assaf Naor, Markov chains in metric spaces and the Lipschitz extension problem. 11:50-12:20 12:20-1:40 Lunch 1:40-2:40 Hari Bercovici, A classical proof of a conformal mapping theorem derived from free probability theory. 2:50-3:50 Alexander Koldobsky, Intersection bodies and $L_p$-spaces. 3:50-4:20 Coffee, Blocker 112 4:30-5:00 Vlad Yaskin, Busemann-Petty problem in hyperbolic and spherical spaces. 5:10-5:40 Masayoshi Kaneda, Extreme points of the unit ball of a quasi-multiplier space 6:30- Dinner at Imperial Chinese Restaurant, 2232 S. Texas Ave. Sunday, August 8 Blocker 120 9:30-10:00 Coffee & Donuts, Blocker 112 10:00-11:00 Stephen Semmes, Happy fractals. 11:10-12:10 Staszek Szarek, Questions in convexity and geometry of Banach spaces related to quantum information theory. 12:20-12:50 George Androulakis, Embedding L_infinity into the space of all operators on certain Banach spaces.

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Abstract of a paper by Vladimir Pestov
by Dale Alspach 27 Jul '04

27 Jul '04

This is an announcement for the paper "Oscillation stability of the Urysohn metric space" by Vladimir Pestov. Abstract: We outline general concepts of oscillation stability and distortion for spaces with action of a topological transformation group, and survey a number of examples. We observe that the universal Urysohn metric space $\U$ (viewed as a homogeneous factor-space of its group of isometries) is oscillation stable, that is, for every bounded uniformly continuous function $f\colon\U\to\R$ and each $\e>0$ there is an isometric copy $\U^\prime\subset\U$ of $\U$, such that $f\vert_{\U^\prime}$ is constant to within $\e$. This stands in marked contrast to the unit sphere $\s^\infty$ of the Hilbert space $\ell^2$, which is a universal analogue of $\U$ in the class of spherical metric spaces, but has the distortion property according to a well-known result by Odell and Schlumprecht. Archive classification: Functional Analysis Mathematics Subject Classification: 05C55; 22F30; 43A85; 46B20; 54E35; 54H15 Remarks: 10 pages, LaTeX 2e The source file(s), osc.tex: 48054 bytes, is(are) stored in gzipped form as 0407444.gz with size 16kb. The corresponding postcript file has gzipped size 63kb. Submitted from: vpest283(a)uottawa.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407444 or http://arXiv.org/abs/math.FA/0407444 or by email in unzipped form by transmitting an empty message with subject line uget 0407444 or in gzipped form by using subject line get 0407444 to: math(a)arXiv.org.

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Abstract of a paper by David Kerr and Hanfeng Li
by Dale Alspach 23 Jul '04

23 Jul '04

This is an announcement for the paper "Dynamical entropy in Banach spaces" by David Kerr and Hanfeng Li. Abstract: We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometrically and topologically. This leads to various applications; for example, we obtain a geometric description of the topological Pinsker factor and show that a C*-algebra is type I if and only if every multiplier inner *-automorphism has zero CA entropy. We also examine the behaviour of CA entropy under various product constructions and determine its value in many examples, including isometric automorphisms of l_p spaces and noncommutative tensor product shifts. Archive classification: Functional Analysis; Dynamical Systems; Operator Algebras Remarks: 40 pages; subsumes the material from math.DS/0303161 The source file(s), CA13.tex: 144163 bytes, is(are) stored in gzipped form as 0407386.gz with size 41kb. The corresponding postcript file has gzipped size 162kb. Submitted from: kerr(a)math.uni-muenster.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407386 or http://arXiv.org/abs/math.FA/0407386 or by email in unzipped form by transmitting an empty message with subject line uget 0407386 or in gzipped form by using subject line get 0407386 to: math(a)arXiv.org.

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SUMIRFAS Announcement
by Bill Johnson 19 Jul '04

19 Jul '04

ANNOUNCEMENT OF SUMIRFAS 2004 The Informal Regional Functional Analysis Seminar August 6 - 8 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Linear Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ Below is a list of speakers, current as of July 18. The Home Page also contains other information about the Workshop, including a list of participants and a schedule of seminars. Housing: Contact Cheryl Williams, (cherylr(a)math.tamu.edu; 979/845-9424, office; 979/ 845-6028, fax) for help with housing. Please tell Cheryl the type of accommodation you desire (smoking or nonsmoking). We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cheryl to book your room, please tell her if you are requesting support. Dinner: There will be a dinner at 6:30 p.m. on Saturday, August 7, at Imperial Chinese Restaurant, 2232 S. Texas Ave. in College Station. The cost for the subsidized dinner is $15 per person for faculty and accompanying persons and $10 per person for student participants. Please tell Cheryl Dorn if you (and spouse or companion, if applicable) will attend. Checks should be made out to Math. Dept., TAMU. ** DINNER RESERVATIONS SHOULD BE MADE BY August 2 and PAYMENT MADE BY August 6. ** W. Johnson, johnson(a)math.tamu.edu K. Dykema, kdykema(a)math.tamu.edu D. Larson, larson(a)math.tamu.edu G. Pisier,pisier(a)math.tamu.edu J. Zinn, jzinn(a)math.tamu.edu SUMIRFAS talks (as of July 18) Hari Bercovici, A classical proof of a conformal mapping theorem derived from free probability theory Uffe Haagerup, Random Matrices and C*-algebras Alexander Koldobsky, Intersection bodies and $L_p$-spaces Michael Lacey, Hankel Operators and Product BMO Narutaka Ozawa, New progress in the classification of group von Neumann algebras Assaf Naor, Markov chains in metric spaces and the Lipschitz extension problem Stanislaw Szarek, (not yet confirmed)

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Abstract of a paper by Julio Becerra-Guerrero and Miguel Martin
by Dale Alspach 16 Jul '04

16 Jul '04

This is an announcement for the paper "The Daugavet property of $C^*$-algebras, $JB^*$-triples, and of their isometric preduals" by Julio Becerra-Guerrero and Miguel Martin. Abstract: A Banach space $X$ is said to have the Daugavet property if every rank-one operator $T:X\longrightarrow X$ satisfies $\|Id + T\| = 1 + \|T\|$. We give geometric characterizations of this property in the settings of $C^*$-algebras, $JB^*$-triples and their isometric preduals. We also show that, in these settings, the Daugavet property passes to ultrapowers, and thus, it is equivalent to an stronger property called the uniform Daugavet property. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: Primary 17C; 46B04; 46B20; 46L05; 46L70; Secondary 46B22, 46M07 Remarks: 18 pages The source file(s), BeceMart.tex: 68626 bytes, is(are) stored in gzipped form as 0407214.gz with size 19kb. The corresponding postcript file has gzipped size 90kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407214 or http://arXiv.org/abs/math.FA/0407214 or by email in unzipped form by transmitting an empty message with subject line uget 0407214 or in gzipped form by using subject line get 0407214 to: math(a)arXiv.org.

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Abstract of a paper by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann
by Dale Alspach 15 Jul '04

15 Jul '04

This is an announcement for the paper "Saturating constructions for normed spaces II" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann. Abstract: We prove several results of the following type: given finite dimensional normed space V possessing certain geometric property there exists another space X having the same property and such that (1) log(dim X) = O(log(dim V)) and (2) every subspace of X, whose dimension is not "too small," contains a further well-complemented subspace nearly isometric to V. This sheds new light on the structure of large subspaces or quotients of normed spaces (resp., large sections or linear images of convex bodies) and provides definitive solutions to several problems stated in the 1980s by V. Milman. The proofs are probabilistic and depend on careful analysis of images of convex sets under Gaussian linear maps. Archive classification: Functional Analysis; Probability Mathematics Subject Classification: 46B20; 46B07; 52A21; 52A22; 60D05 Remarks: 35 p., LATEX The source file(s), SzarekTomczakSat2.tex: 104176 bytes, is(are) stored in gzipped form as 0407234.gz with size 33kb. The corresponding postcript file has gzipped size 127kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407234 or http://arXiv.org/abs/math.FA/0407234 or by email in unzipped form by transmitting an empty message with subject line uget 0407234 or in gzipped form by using subject line get 0407234 to: math(a)arXiv.org.

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Abstract of a paper by Stanislaw J. Szarek, and Nicole Tomczak-Jaegermann
by Dale Alspach 15 Jul '04

15 Jul '04

This is an announcement for the paper "Saturating constructions for normed spaces" by Stanislaw J. Szarek and Nicole Tomczak-Jaegermann . Abstract: We prove several results of the following type: given finite dimensional normed space V there exists another space X with log(dim X) = O(log(dim V)) and such that every subspace (or quotient) of X, whose dimension is not "too small," contains a further subspace isometric to V. This sheds new light on the structure of such large subspaces or quotients (resp., large sections or projections of convex bodies) and allows to solve several problems stated in the 1980s by V. Milman. The proofs are probabilistic and depend on careful analysis of images of convex sets under Gaussian linear maps. Archive classification: Functional Analysis; Probability Mathematics Subject Classification: 46B20; 52A21; 52A22; 60D05 Remarks: 27 p., LATEX The source file(s), SzarekTomczakSat1.tex: 71711 bytes, is(are) stored in gzipped form as 0407233.gz with size 25kb. The corresponding postcript file has gzipped size 105kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407233 or http://arXiv.org/abs/math.FA/0407233 or by email in unzipped form by transmitting an empty message with subject line uget 0407233 or in gzipped form by using subject line get 0407233 to: math(a)arXiv.org.

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[Banach] Abstract of a paper by S. Artstein, V. Milman, S. J. Szarek, and N. Tomczak-Jaegermann
by Dale Alspach 15 Jul '04

15 Jul '04

This is an announcement for the paper "On convexified packing and entropy duality" by S. Artstein, V. Milman, S. J. Szarek, and N. Tomczak-Jaegermann. Abstract: For a compact operator acting between two Banach spaces, a 1972 duality conjecture due to Pietsch asserts that its entropy numbers and those of its adjoint are equivalent. This is equivalent to a dimension-free inequality relating covering (or packing) numbers for convex bodies to those of their polars. The duality conjecture has been recently proved (see math.FA/0407236) in the central case when one of the Banach spaces is Hilbertian, which - in the geometric setting - corresponds to a duality result for symmetric convex bodies in Euclidean spaces. In the present paper we define a new notion of "convexified packing," show a duality theorem for that notion, and use it to prove the duality conjecture under much milder conditions on the spaces involved (namely, that one of them is K-convex). Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 46B10; 46B07; 46B50; 47A05; 52C17; 51F99 Remarks: 6 p., LATEX The source file(s), ConvPackShort5.tex: 21620 bytes, is(are) stored in gzipped form as 0407238.gz with size 8kb. The corresponding postcript file has gzipped size 43kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407238 or http://arXiv.org/abs/math.FA/0407238 or by email in unzipped form by transmitting an empty message with subject line uget 0407238 or in gzipped form by using subject line get 0407238 to: math(a)arXiv.org.

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Abstract of a paper by S. Artstein, V. Milman, and S. J. Szarek
by Dale Alspach 15 Jul '04

15 Jul '04

This is an announcement for the paper "Duality of metric entropy" by S. Artstein, V. Milman, and S. J. Szarek. Abstract: For two convex bodies K and T in $R^n$, the covering number of K by T, denoted N(K,T), is defined as the minimal number of translates of T needed to cover K. Let us denote by $K^o$ the polar body of K and by D the euclidean unit ball in $R^n$. We prove that the two functions of t, N(K,tD) and N(D, tK^o), are equivalent in the appropriate sense, uniformly over symmetric convex bodies K in $R^n$ and over positive integers n. In particular, this verifies the duality conjecture for entropy numbers of linear operators, posed by Pietsch in 1972, in the central case when either the domain or the range of the operator is a Hilbert space. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 46B10; 47A05; 52C17; 51F99 Remarks: 17 p., LATEX The source file(s), ArtMilSzaAoM.tex: 40692 bytes, is(are) stored in gzipped form as 0407236.gz with size 14kb. The corresponding postcript file has gzipped size 68kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407236 or http://arXiv.org/abs/math.FA/0407236 or by email in unzipped form by transmitting an empty message with subject line uget 0407236 or in gzipped form by using subject line get 0407236 to: math(a)arXiv.org.

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Abstract of a paper by Stanislaw Szarek
by Dale Alspach 14 Jul '04

14 Jul '04

This is an announcement for the paper "The volume of separable states is super-doubly-exponentially small" by Stanislaw Szarek. Abstract: In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the "effective radius" of that set in the sense of volume is determined up to a factor which is a (small) power of N, and thus precisely on the scale of powers of its dimension. Additionally, one of the appendices contains sharp estimates (by known methods) for the expected values of norms of the GUE random matrices. We employ standard tools of classical convexity, high-dimensional probability and geometry of Banach spaces. Archive classification: Quantum Physics; Functional Analysis Remarks: 20 p., LATEX; an expanded version of the original submission: more background material from convexity and geometry of Banach spaces, more exhaustive bibliography and improved quality of references to the bibliography The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/quant-ph/0310061 or http://arXiv.org/abs/quant-ph/0310061 or by email in unzipped form by transmitting an empty message with subject line uget /0310061 or in gzipped form by using subject line get /0310061 to: math(a)arXiv.org.

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Abstract of a paper by Jeremy J. Becnel
by Dale Alspach 13 Jul '04

13 Jul '04

This is an announcement for the paper "About countably-normed spaces" by Jeremy J. Becnel. Abstract: Here we present an overview of countably normed spaces. In particular, we discuss the main topologies---weak, strong, inductive, and Mackey---placed on the dual of a countably normed spaces and discuss the sigma fields generated by these topologies. In particlar, we show that the strong, inductive, and Mackey topologies are equivalent under reasonable conditions. Also we show that all four topologies induce the same Borel field under certain conditions. The purpose in mind is to provide the background material for many of the results used in White Noise Analysis. Archive classification: Functional Analysis Mathematics Subject Classification: 46A11 Remarks: 23 pages, 0 figures, Background material for White Noise Analysis The source file(s), NuclearSpace.bbl: 1198 bytes, NuclearSpace.tex: 1472 bytes, borel.tex: 5271 bytes, cns.tex: 16479 bytes, compare.tex: 6600 bytes, conclusion.tex: 4430 bytes, inductive.tex: 6567 bytes, nuclear.sty: 4578 bytes, strong.tex: 17400 bytes, tvs.tex: 14418 bytes, weak.tex: 3536 bytes, is(are) stored in gzipped form as 0407200.tar.gz with size 23kb. The corresponding postcript file has gzipped size 103kb. Submitted from: beck(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407200 or http://arXiv.org/abs/math.FA/0407200 or by email in unzipped form by transmitting an empty message with subject line uget 0407200 or in gzipped form by using subject line get 0407200 to: math(a)arXiv.org.

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Abstract of a paper by Christian Rosendal
by Dale Alspach 08 Jul '04

08 Jul '04

This is an announcement for the paper "Incomparable, non isomorphic and minimal Banach spaces" by Christian Rosendal. Abstract: A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes and has an isomorphically homogeneous subsequence. Archive classification: Functional Analysis; Logic The source file(s), ArchiveIncomparable.tex: 57150 bytes, is(are) stored in gzipped form as 0407111.gz with size 19kb. The corresponding postcript file has gzipped size 81kb. Submitted from: rosendal(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0407111 or http://arXiv.org/abs/math.FA/0407111 or by email in unzipped form by transmitting an empty message with subject line uget 0407111 or in gzipped form by using subject line get 0407111 to: math(a)arXiv.org.

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Banach July 2004