Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by W. B. Johnson and Bentuo Zheng
by Dale Alspach 08 Feb '07

08 Feb '07

This is an announcement for the paper "A characterization of subspaces and quotients of reflexive Banach spaces with unconditional basis" by W. B. Johnson and Bentuo Zheng. Abstract: We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient of a reflexive Banach space with an unconditional finite dimensional decomposition embeds into a reflexive Banach space with an unconditional basis. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03 The source file(s), JZh10.tex: 38045 bytes, is(are) stored in gzipped form as 0702199.gz with size 11kb. The corresponding postcript file has gzipped size 96kb. Submitted from: btzheng(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0702199 or http://arXiv.org/abs/math.FA/0702199 or by email in unzipped form by transmitting an empty message with subject line uget 0702199 or in gzipped form by using subject line get 0702199 to: math(a)arXiv.org.

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Workshop in Analysis and Probability at A&M
by Bill Johnson 01 Feb '07

01 Feb '07

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2007 The Summer 2007 session of the Workshop in Analysis and Probability at Texas A&M University will be in session from July 9 until August 12. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 10-12. Speakers will include Rodrigo Banuelos, Grahame Bennett, Dmitry Panchenko, Michael Steele, and Staszek Szarek. Ken Dykema <kdykema(a)math.tamu.edu> and Michael Anshelevich <manshel(a)math.tamu.edu> are organizing a Concentration Week on "Free Probability Theory" which is designed to introduce advanced graduate students and postdocs to Free Probability. It will take place July 9-13. There will be one or two basic talks at the start for those without any previous knowledge of free probability theory. Then lecture series will be given by the following experts: Hari Bercovici, "Complex analytic and probabalistic aspects of free probability theory"; Kenley Jung, "Free entropy and operator algebras"; Alexandru Nica, "Combinatorics of free probability theory". Gideon Schechtman <gideon.schechtman(a)weizmann.ac.il> and Joel Zinn <jzinn(a)math.tamu.edu> are organizing a Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena" that will take place August 6 - August 10. The first day will be devoted to introductory talks designed to introduce non experts to the subject. The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu> or Jaime Vykukal <jaime(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Larson <larson(a)math.tamu.edu>, Gilles Pisier <pisier(a)math.tamu.edu>, or Joel Zinn <jzinn(a)math.tamu.edu>. For information about the Concentration Week "Free Probability Theory" contact Michael Anshelevich <manshel(a)math.tamu.edu> or Ken Dykema <kdykema(a)math.tamu.edu>. For information about the Concentration Week on "Probability Inequalities with Applications to High Dimensional Phenomena", contact Joel Zinn <jzinn(a)math.tamu.edu>.

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Abstract of a paper by Ludvek Zajivcek
by Dale Alspach 01 Feb '07

01 Feb '07

This is an announcement for the paper "On Lipschitz and d.c. surfaces of finite codimension in a Banach space" by Ludvek Zajivcek. Abstract: Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract approximation theory. Using these properties, we improve an unpublished result of M. Heisler which gives an alternative proof of a result of D. Preiss on singular points of convex functions. Archive classification: Functional Analysis Mathematics Subject Classification: 46T05, 58C20, 47H05 Remarks: 13 pages The source file(s), ZAJICEK2.TEX: 48703 bytes, is(are) stored in gzipped form as 0701926.gz with size 15kb. The corresponding postcript file has gzipped size 99kb. Submitted from: zajicek(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701926 or http://arXiv.org/abs/math.FA/0701926 or by email in unzipped form by transmitting an empty message with subject line uget 0701926 or in gzipped form by using subject line get 0701926 to: math(a)arXiv.org.

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Abstract of a paper by Emanuel Milman
by Dale Alspach 30 Jan '07

30 Jan '07

This is an announcement for the paper "A solution to a question of A. Koldobsky" by Emanuel Milman. Abstract: In 2000, A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied by the author in [http://www.arxiv.org/math.MG/0512058], providing substantial positive evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This negative answer implies the existence of a non-trivial non-negative function in the range of the spherical Radon transform. Archive classification: Functional Analysis Remarks: 13 pages The source file(s), Solution-To-Koldobsky-Question.bbl: 5474 bytes, Solution-To-Koldobsky-Question.tex: 41825 bytes, is(are) stored in gzipped form as 0701779.tar.gz with size 14kb. The corresponding postcript file has gzipped size 110kb. Submitted from: emanuel.milman(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701779 or http://arXiv.org/abs/math.FA/0701779 or by email in unzipped form by transmitting an empty message with subject line uget 0701779 or in gzipped form by using subject line get 0701779 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg
by Dale Alspach 23 Jan '07

23 Jan '07

This is an announcement for the paper "Rosenthal operator spaces" by Marius Junge, Niels Jorgen Nielsen and Timur Oikhberg. Abstract: In 1969 Lindenstrauss and Rosenthal showed that if a Banach space is isomorphic to a complemented subspace of an L_p-space, then it is either a script L_p-space or isomorphic to a Hilbert space. This is the motivation of this paper where we study non--Hilbertian complemented operator subspaces of non commutative L_p-spaces and show that this class is much richer than in the commutative case. We investigate the local properties of some new classes of operator spaces for every $2<p< \infty$ which can be considered as operator space analogues of the Rosenthal sequence spaces from Banach space theory, constructed in 1970. Under the usual conditions on the defining sequence sigma we prove that most of these spaces are operator script L_p-spaces, not completely isomorphic to previously known such spaces. However it turns out that some column and row versions of our spaces are not operator script L_p-spaces and have a rather complicated local structure which implies that the Lindenstrauss--Rosenthal alternative does not carry over to the non-commutative case. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20;46L07;46L52 The source file(s), njnpart1new11.tex: 38162 bytes, njnpart2new11.tex: 48325 bytes, refnew11.tex: 4840 bytes, rosmatrixnew11.tex: 10401 bytes, uncomp2.tex: 6528 bytes, x3njn1111.tex: 5668 bytes, is(are) stored in gzipped form as 0701480.tar.gz with size 33kb. The corresponding postcript file has gzipped size 176kb. Submitted from: njn(a)imada.sdu.dk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701480 or http://arXiv.org/abs/math.FA/0701480 or by email in unzipped form by transmitting an empty message with subject line uget 0701480 or in gzipped form by using subject line get 0701480 to: math(a)arXiv.org.

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Abstract of a paper by Peter G. Casazza, Dan Edidin, Deepti Kalra and Vern I. Paulsen
by Dale Alspach 23 Jan '07

23 Jan '07

This is an announcement for the paper "Projections and the Kadison-Singer Problem" by Peter G. Casazza, Dan Edidin, Deepti Kalra and Vern I. Paulsen. Abstract: We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures. Archive classification: Functional Analysis Mathematics Subject Classification: 46L15; 47L25 The source file(s), 127.Projks.tex: 48714 bytes, is(are) stored in gzipped form as 0701450.gz with size 16kb. The corresponding postcript file has gzipped size 123kb. Submitted from: pete(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701450 or http://arXiv.org/abs/math.FA/0701450 or by email in unzipped form by transmitting an empty message with subject line uget 0701450 or in gzipped form by using subject line get 0701450 to: math(a)arXiv.org.

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Abstract of a paper by George Androulakis and Frank Sanacory
by Dale Alspach 16 Jan '07

16 Jan '07

This is an announcement for the paper "On the ``Multiple of the Inclusion Plus Compact'' problem" by George Androulakis and Frank Sanacory. Abstract: The ``multiple of the inclusion plus compact problem'' which was posed by T.W.~Gowers in 1996 and Th.~Schlumprecht in 2003, asks whether for every infinite dimensional Banach space $X$ there exists a closed subspace $Y$ of $X$ and a bounded linear operator from $Y$ to $X$ which is not a compact perturbation of a multiple of the inclusion map from $Y$ to $X$. We give sufficient conditions on the spreading models of seminormalized basic sequences of a Banach space $X$ which guarantee that the ``multiple of the inclusion plus compact'' problem has an affirmative answer for $X$. Our results strengthen a previous result of the first named author, E.~Odell, Th.~Schlumprecht and N.~Tomczak-Jaegermann as well as a result of Th.~Schlumprecht. We give an example of a Hereditarily Indecomposable Banach space where our results apply. For the proof of our main result we use an extension of E.~Odell's Schreier unconditionality result for arrays. Archive classification: Functional Analysis Mathematics Subject Classification: 46A32, 47B07 The source file(s), lambdaipluscpt.tex: 114786 bytes, is(are) stored in gzipped form as 0701354.gz with size 28kb. The corresponding postcript file has gzipped size 203kb. Submitted from: giorgis(a)math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701354 or http://arXiv.org/abs/math.FA/0701354 or by email in unzipped form by transmitting an empty message with subject line uget 0701354 or in gzipped form by using subject line get 0701354 to: math(a)arXiv.org.

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Abstract of a paper by E. Odell and Th. Schlumprecht
by Dale Alspach 12 Jan '07

12 Jan '07

This is an announcement for the paper "Embedding into Banach spaces with finite dimensional decompositions" by E. Odell and Th. Schlumprecht. Abstract: This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having property (P), or more generally, having a property related to (P)? Secondly, given a class of Banach spaces, does there exist a Banach space in this class, or in a closely related one, which is universal for this class? Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; 46B20 Remarks: 26 pages The source file(s), os-embedding-final.tex: 109527 bytes, is(are) stored in gzipped form as 0701324.gz with size 33kb. The corresponding postcript file has gzipped size 182kb. 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/0701324 or http://arXiv.org/abs/math.FA/0701324 or by email in unzipped form by transmitting an empty message with subject line uget 0701324 or in gzipped form by using subject line get 0701324 to: math(a)arXiv.org.

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Abstract of a paper by Boris Rubin
by Dale Alspach 12 Jan '07

12 Jan '07

This is an announcement for the paper "The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry" by Boris Rubin. Abstract: The lower dimensional Busemann-Petty problem asks, whether $n$-dimensional origin-symmetric convex bodies, having smaller $i$-dimensional sections, necessarily have smaller volumes. For $i=1$, the affirmative answer is obvious. For $i>3$, the answer is negative. For $i=2$ and $i=3$, the problem is still open, except when the body with smaller sections is a body of revolution. In this case the answer is affirmative. The paper contains a complete solution to the problem in the more general situation, when the body with smaller sections is invariant under orthogonal transformations preserving coordinate subspaces $R^{l}$ and $R^{n-l}$ of $R^{n}$ for arbitrary fixed $0<l<n$. Archive classification: Functional Analysis Mathematics Subject Classification: 44A12; 52A38 Remarks: 26 pages The source file(s), simplex2.tex: 72011 bytes, is(are) stored in gzipped form as 0701317.gz with size 23kb. The corresponding postcript file has gzipped size 155kb. Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701317 or http://arXiv.org/abs/math.FA/0701317 or by email in unzipped form by transmitting an empty message with subject line uget 0701317 or in gzipped form by using subject line get 0701317 to: math(a)arXiv.org.

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Abstract of a paper by Shachar Lovett and Sasha Sodin
by Dale Alspach 10 Jan '07

10 Jan '07

This is an announcement for the paper "Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits" by Shachar Lovett and Sasha Sodin. Abstract: It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Extending earlier work by Artstein--Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits. Archive classification: Functional Analysis; Metric Geometry; Probability Remarks: 16 pages The source file(s), derand.tex: 32081 bytes, is(are) stored in gzipped form as 0701102.gz with size 11kb. The corresponding postcript file has gzipped size 109kb. Submitted from: sodinale(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701102 or http://arXiv.org/abs/math.FA/0701102 or by email in unzipped form by transmitting an empty message with subject line uget 0701102 or in gzipped form by using subject line get 0701102 to: math(a)arXiv.org.

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