Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Magdalena Musat
by Dale Alspach 07 Jan '05

07 Jan '05

This is an announcement for the paper "On the operator space UMD property for noncommutative Lp-spaces" by Magdalena Musat. Abstract: We study the operator space UMD property, introduced by Pisier in the context of noncommutative vector-valued Lp-spaces. It is unknown whether the property is independent of p in this setting. We prove that for 1<p,q<\infty, the Schatten q-classes Sq are OUMDp. The proof relies on properties of the Haagerup tensor product and complex interpolation. Using ultraproduct techniques, we extend this result to a large class of noncommutative Lq-spaces. Namely, we show that if M is a QWEP von Neumann algebra (i.e., a quotient of a C^*-algebra with Lance's weak expectation property) equipped with a normal, faithful tracial state \tau, then Lq(M,\tau) is OUMDp for 1<p,q<\infty. Archive classification: Operator Algebras; Functional Analysis; Probability Mathematics Subject Classification: 46L52, 47L25 (Primary) 60G46 (Secondary) Remarks: 30 pages The source file(s), OUMDLP.TEX: 120786 bytes, is(are) stored in gzipped form as 0501033.gz with size 33kb. The corresponding postcript file has gzipped size 135kb. Submitted from: mmusat(a)math.ucsd.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0501033 or http://arXiv.org/abs/math.OA/0501033 or by email in unzipped form by transmitting an empty message with subject line uget 0501033 or in gzipped form by using subject line get 0501033 to: math(a)arXiv.org.

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Abstract of a paper by Biagio Ricceri
by Dale Alspach 07 Jan '05

07 Jan '05

This is an announcement for the paper "Some research perspectives in nonlinear functional analysis" by Biagio Ricceri. Abstract: The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings, fixed points, critical points, global minima, control theory. Archive classification: Functional Analysis Mathematics Subject Classification: 46N10, 47H10 Citation: Semin. Fixed Point Theory Cluj-Napoca 3, 99-110 (2002) Remarks: 13 pages The source file(s), idec-62.tex: 26131 bytes, is(are) stored in gzipped form as 0412564.gz with size 8kb. The corresponding postcript file has gzipped size 42kb. Submitted from: elliott(a)mail.mathatlas.yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412564 or http://arXiv.org/abs/math.FA/0412564 or by email in unzipped form by transmitting an empty message with subject line uget 0412564 or in gzipped form by using subject line get 0412564 to: math(a)arXiv.org.

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Abstract of a paper by Biagio Ricceri
by Dale Alspach 07 Jan '05

07 Jan '05

This is an announcement for the paper "Covering dimension and nonlinear equations" by Biagio Ricceri. Abstract: Theorem: Let X and Y be two Banach spaces, Phi: X to Y a continuous, linear, surjective operator, and Psi: X to Y a completely continuous operator with bounded range. Then, one has dim{x in X : Phi(x)=Psi(x)} >= dim(Phi^{-1}(0)). Here dim denotes the covering dimension. Archive classification: Functional Analysis Mathematics Subject Classification: 47J05, 47H10 Citation: RIMS Kokyuroku 1031, 97-100 (1998) Remarks: 3 pages The source file(s), paam-15.tex: 7189 bytes, is(are) stored in gzipped form as 0412563.gz with size 3kb. The corresponding postcript file has gzipped size 26kb. Submitted from: elliott(a)mail.mathatlas.yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412563 or http://arXiv.org/abs/math.FA/0412563 or by email in unzipped form by transmitting an empty message with subject line uget 0412563 or in gzipped form by using subject line get 0412563 to: math(a)arXiv.org.

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Abstract of a paper by Dmitry B. Rokhlin
by Dale Alspach 07 Jan '05

07 Jan '05

This is an announcement for the paper "The Kreps-Yan theorem for $L^\infty$" by Dmitry B. Rokhlin. Abstract: We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone $C\subset L^\infty$ such that $C\cap L_+^\infty=\{0\}$ and $C\supset -L_+^\infty$, there exists a strictly positive continuous linear functional, whose restriction on $C$ is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindel\"of Banach space, where such approach is not needed. Archive classification: Functional Analysis Mathematics Subject Classification: 46E30; 46B40 Remarks: 8 pages The source file(s), rok_KY.TEX: 18051 bytes, is(are) stored in gzipped form as 0412551.gz with size 7kb. The corresponding postcript file has gzipped size 45kb. Submitted from: rokhlin(a)math.rsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412551 or http://arXiv.org/abs/math.FA/0412551 or by email in unzipped form by transmitting an empty message with subject line uget 0412551 or in gzipped form by using subject line get 0412551 to: math(a)arXiv.org.

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Abstract of a paper by Ioannis Gasparis
by Dale Alspach 22 Dec '04

22 Dec '04

This is an announcement for the paper "Operators on $C[0,1]$ preserving copies of asymptotic $\ell_1$ spaces" by Ioannis Gasparis. Abstract: It is shown that every operator on $C[0,1]$ which preserves a copy of an asymptotic $\ell_1$ space, also preserves a copy of $C[0,1]$. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03 The source file(s), asymp.tex: 73653 bytes, is(are) stored in gzipped form as 0412426.gz with size 20kb. The corresponding postcript file has gzipped size 100kb. Submitted from: ioagaspa(a)math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412426 or http://arXiv.org/abs/math.FA/0412426 or by email in unzipped form by transmitting an empty message with subject line uget 0412426 or in gzipped form by using subject line get 0412426 to: math(a)arXiv.org.

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Abstract of a paper by N.J.Kalton, A.Koldobsky, V.Yaskin and M.Yaskina
by Dale Alspach 21 Dec '04

21 Dec '04

This is an announcement for the paper "The geometry of $L_0$" by N.J.Kalton, A.Koldobsky, V.Yaskin and M.Yaskina. Abstract: Suppose that we have the unit Euclidean ball in $\R^n$ and construct new bodies using three operations - linear transformations, closure in the radial metric and multiplicative summation defined by $\|x\|_{K+_0L} = \sqrt{\|x\|_K\|x\|_L}.$ We prove that in dimension 3 this procedure gives all origin symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in $L_0$ that naturally extends the corresponding properties of $L_p$-spaces with $p\ne0$, and show that the procedure described above gives exactly the unit balls of subspaces of $L_0$ in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in $L_0$, and prove several facts confirming the place of $L_0$ in the scale of $L_p$-spaces. Archive classification: Functional Analysis; Metric Geometry Mathematics Subject Classification: 46B20, 52Axx Remarks: 21 pages The source file(s), lzero.tex: 51885 bytes, is(are) stored in gzipped form as 0412371.gz with size 15kb. The corresponding postcript file has gzipped size 80kb. Submitted from: yaskinv(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0412371 or http://arXiv.org/abs/math.FA/0412371 or by email in unzipped form by transmitting an empty message with subject line uget 0412371 or in gzipped form by using subject line get 0412371 to: math(a)arXiv.org.

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Summer School and Conference
by Dale Alspach 15 Dec '04

15 Dec '04

This is a preliminary announcement about two (separate) events that will take place at the Hebrew University in June 2005. The Institute of Advanced Studies (IAS) of the Hebrew University organizes a conference titled "Contemporary Ramifications of Banach Space Theory" in honour of Joram Lindenstrauss and Lior Tzafriri on the occasion of their retirement. The conference will be held June 19-24, 2005 at the Hebrew University of Jerusalem.The purpose of the conference is to give a survey of many fields that Joram and Lior have made an impact on. Immediately preceeding the conference, on June 14-19, the IAS will organize a summer school (midrasha) devoted to "Connections between probability and geometric functional analysis". The midrasha should be accessible to broader audience, including graduate students in functional analysis. The speakers at the midrasha will be: N.Alon (Tel Aviv) B.Bollobas (Memphis), N.Kalton (Missouri), R.Latala (Warsaw), M.Ledoux (Tulouse), A.Naor (Microsoft), K.Oleszkiewicz (Warsaw), M.Rudelson (Missouri), S.Szarek (Paris), M.Talagrand (Paris). Additional information about these two events can be obtained from Mrs.Pnina Feldman (IAS), e-mail: advanc(a)vms.huji.ac.il or from us, e-mail: bsconf(a)math.huji.ac.il Tomek Szankowski and Morry Zippin, for the organizing committee: Jonathan Arazy(Haifa Univ.) Yoav Benyamini (Technion) Vladimir Fonf (Ben Gurion Univ.) Yoram Gordon (Technion) Vitali Milman (Tel Aviv U.) Gideon Schechtman (Weizmann Institute)

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Abstract of a paper by Miguel Martin
by Dale Alspach 01 Dec '04

01 Dec '04

This is an announcement for the paper "The alternative Daugavet property of $C^*$-algebras and $JB^*$-triples" by Miguel Martin. Abstract: A Banach space $X$ is said to have the alternative Daugavet property if for every (bounded and linear) rank-one operator $T:X\longrightarrow X$ there exists a modulus one scalar $\omega$ such that $\|Id + \omega T\|= 1 + \|T\|$. We give geometric characterizations of this property in the setting of $C^*$-algebras, $JB^*$-triples and their isometric preduals. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46B20, 46L05, 17C65 (primary); 47A12 (secondary) The source file(s), Martin-ADP.tex: 44541 bytes, is(are) stored in gzipped form as 0411555.gz with size 14kb. The corresponding postcript file has gzipped size 69kb. 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/0411555 or http://arXiv.org/abs/math.FA/0411555 or by email in unzipped form by transmitting an empty message with subject line uget 0411555 or in gzipped form by using subject line get 0411555 to: math(a)arXiv.org.

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Announcement: V Conference on Function Spaces
by Krzysztof Jarosz 23 Nov '04

23 Nov '04

Conference Announcement: "Function Spaces V" May 14-19, 2006, Southern Illinois University Edwardsville Topics: Function algebras, Banach algebras, spaces and algebras of analytic functions, Lp spaces, geometry of Banach spaces, isometries of function spaces, and related problems. For more information including funding, principal speakers, registration, travel & housing, and local information please check: http://www.siue.edu/MATH/conference2006/ Or contact: Krzysztof Jarosz Department of Mathematics & Statistics SIUE Edwardsville, Illinois 62026-1653, USA kjarosz(a)siue.edu

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Winter School, Toulouse 2005
by Dale Alspach 19 Nov '04

19 Nov '04

Second Announcement of the Winter School on PROBABILISTIC METHODS IN HIGH DIMENSION PHENOMENA Toulouse, January 10-14, 2005 The school will provide young as well as expert scientists with the recent probabilistic tools developed for the investigation of high-dimensional systems. It is part of the European Network "Phenomena in High Dimension". It will be composed of the following five courses: I.Benjamini (Rehovot) ``Random walks and Percolation on graphs'' C.Borell (Goteborg) ``Minkowski sums in Gaussian analysis'' K.Johansson (Stockholm) ``Determinantal Processes in Random Matrix Theory'' G.Lugosi (Barcelona) ``Concentration of Functions of Independent Random Variables'' R.Schneider (Freiburg) ``Convexity in Stochastic Geometry'' It is now time for participants: * to registrate: we had some technical problems with the online registration engine. So we ask you to registrate (to REGISTRATE AGAIN if you already did it through the online form) by sending an email to our secretary Mrs Michel michel(a)lsp.ups-tlse.fr, specifying your NAME, your AFFILIATION, ADDRESS and DATES of attendance. * and to prepare their travel and accomodation plans: The expenses of the members of the PHD network are supported by their nodes (but it is likely that universities have to pay in advance and the RTN will reimburse when it is operating). We hope that we will have some money left to partially cover the expenses of participants not belonging to the network. Priority will be given to PHD Students and Post-Docs. If you need such support, please mention it in the registration email to Mrs Michel. More information is available on the conference Webpage http://www.lsp.ups-tlse.fr/Proba_Winter_School/ It has been updated and contains new pieces of information about * abstracts of the courses * accomodation: The list of hotels has been completed. Economical options have been added. In particular we have made a temporary reservation for a very limited number of rooms on the campus for 22 Euros per night. These rooms can be booked by sending an email to Mrs Michel (michel(a)lesp.ups-tlse.fr). Sincerely, F. Barthe M. Ledoux - ------------------------------------------------------------------------------ Institut de Mathematiques - Universite Paul Sabatier - Toulouse III 118 route de Narbonne - 31062 Toulouse Cedex 4 - FRANCE. __________________________________________________________________________ Michel Ledoux ledoux(a)math.ups-tlse.fr Institut de Mathematiques Tel : (+33) 561 55 85 74 Universite de Toulouse Fax : (+33) 561 55 60 89 F-31062 Toulouse, France http://www.lsp.ups-tlse.fr/Ledoux/

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