Banach March 2008

banach@mathdept.okstate.edu

2 participants
11 discussions

Abstract of a paper by Michael Cwikel
by alspach＠fourier.math.okstate.edu 26 Mar '08

26 Mar '08

This is an announcement for the paper "Lecture notes on duality and interpolation spaces" by Michael Cwikel. Abstract: Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals of his complex interpolation spaces [A_0,A_1]_\theta. The pace is slow, since these notes are intended for graduate students who have just begun to study interpolation spaces. Archive classification: math.FA Mathematics Subject Classification: 46B70 (primary) 46B10 (secondary) Remarks: 24 pages The source file(s), NotesOnDuality-arXiv.tex: 93949 bytes, is(are) stored in gzipped form as 0803.3558.gz with size 25kb. The corresponding postcript file has gzipped size 138kb. Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3558 or http://arXiv.org/abs/0803.3558 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3558 or in gzipped form by using subject line get 0803.3558 to: math(a)arXiv.org.

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Abstract of a paper by Jarno Talponen
by alspach＠fourier.math.okstate.edu 26 Mar '08

26 Mar '08

This is an announcement for the paper "Lindelof type of generalization of separability in Banach spaces" by Jarno Talponen. Abstract: We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of \mathcal{F}. All separable Banach spaces have CSP and plenty of examples of non-separable CSP spaces are provided. Connections of CSP with Markucevic-bases, Corson property and related geometric issues are discussed. Archive classification: math.FA Mathematics Subject Classification: 46B26; 46A50 The source file(s), csp.tex: 62263 bytes, is(are) stored in gzipped form as 0803.3541.gz with size 17kb. The corresponding postcript file has gzipped size 108kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3541 or http://arXiv.org/abs/0803.3541 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3541 or in gzipped form by using subject line get 0803.3541 to: math(a)arXiv.org.

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Abstract of a paper by Marianne Morillon
by alspach＠fourier.math.okstate.edu 26 Mar '08

26 Mar '08

This is an announcement for the paper "Countable choice and compactness" by Marianne Morillon. Abstract: We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p greater or equal to 1 (resp. . p = 0), and some closed subset F of [0, 1]^I which is a bounded subset of l^p(I), we show that AC(N) (resp. DC, the axiom of Dependent Choices) implies the compactness of F. Archive classification: math.FA math.GN math.LO Mathematics Subject Classification: 03E25, 46B26, 54D30 The source file(s), figure.tex: 548 bytes final.bbl: 2612 bytes final.tex: 55144 bytes icone-ermit.eps: 24310 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.3131 or http://arXiv.org/abs/0803.3131 or by email in unzipped form by transmitting an empty message with subject line uget 0803.3131 or in gzipped form by using subject line get 0803.3131 to: math(a)arXiv.org.

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Abstract of a paper by Ian Doust and Venta Terauds
by alspach＠fourier.math.okstate.edu 21 Mar '08

21 Mar '08

This is an announcement for the paper "Extensions of an $AC(\sigma)$ functional calculus" by Ian Doust and Venta Terauds. Abstract: On a reflexive Banach space $X$, if an operator $T$ admits a functional calculus for the absolutely continuous functions on its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an $\AC$ functional calculus is possible for operators acting on families of interpolation spaces such as the $L^p$ spaces. Archive classification: math.FA Mathematics Subject Classification: 47B40 The source file(s), extns-f-submit.tex: 36353 bytes, is(are) stored in gzipped form as 0803.2131.gz with size 11kb. The corresponding postcript file has gzipped size 84kb. Submitted from: i.doust(a)unsw.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.2131 or http://arXiv.org/abs/0803.2131 or by email in unzipped form by transmitting an empty message with subject line uget 0803.2131 or in gzipped form by using subject line get 0803.2131 to: math(a)arXiv.org.

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Abstract of a paper by Manor Mendel and Assaf Naor
by alspach＠fourier.math.okstate.edu 14 Mar '08

14 Mar '08

This is an announcement for the paper "Markov convexity and local rigidity of distorted metrics" by Manor Mendel and Assaf Naor. Abstract: The geometry of discrete tree metrics is studied from the following perspectives: 1. Markov p-convexity, which was shown by Lee, Naor, and Peres to be a property of p-convex Banach space, is shown here to be equivalent to p-convexity of Banach spaces. 2. On the other hand, there exists an example of a metric space which is not Markov p-convex for any finite p, but does not uniformly contain complete binary trees. Note that the previous item implies that Banach spaces contain complete binary trees uniformly if and only if they are not Markov p-convex for any finite p. 3. For every B>4, a metric space X is constructed such that all tree metrics can be embedded in X with distortion at most B, but when large complete binary trees are embedded in X, the distortion tends to B. Therefore the class of finite tree metrics do exhibit a dichotomy in the distortions achievable when embedding them in other metric spaces. This is in contrast to the dichotomy exhibited by the class of finite subsets of L_1, and the class of all finite metric spaces. Archive classification: math.MG math.FA Remarks: 10 pages, extended abstract to appear in SoCG '08 %The source file(s), Charlie-tree-socg.bbl: 8435 bytes Charlie-tree-socg.tex: 150202 bytes figs/3path-types.eps: 26109 bytes figs/3path-types.pdf: 13428 bytes figs/d_e-metric.eps: 27160 bytes figs/d_e-metric.pdf: 16009 bytes figs/fork-types.eps: 25081 bytes figs/fork-types.pdf: 12092 bytes figs/lang.eps: 30961 bytes figs/lang.pdf: 14246 bytes figs/mid-lemma1.eps: 18989 bytes figs/mid-lemma1.pdf: 10463 bytes figs/mid-lemma2-c1a.eps: 21267 bytes figs/mid-lemma2-c1a.pdf: 12517 bytes figs/mid-lemma2-c1b.eps: 18219 bytes figs/mid-lemma2-c1b.pdf: 10695 bytes figs/mid-lemma2-c1c.eps: 21626 bytes figs/mid-lemma2-c1c.pdf: 12610 bytes figs/mid-lemma2-c2a.eps: 24273 bytes figs/mid-lemma2-c2a.pdf: 14271 bytes figs/mid-lemma2-c2b.eps: 18207 bytes figs/mid-lemma2-c2b.pdf: 10699 bytes figs/mid-lemma2-c2c.eps: 21237 bytes figs/mid-lemma2-c2c.pdf: 12496 bytes figs/midpoints-new.eps: 17442 bytes figs/midpoints-new.pdf: 9662 bytes figs/tip-contract.eps: 13542 bytes figs/tip-contract.pdf: 6745 bytes figs/type-II-surprise.eps: 17919 bytes figs/type-II-where-w.eps: 11124 bytes sig-alt-full.cls: 56035 bytes, is(are) stored in gzipped form as 0803.1697.tar.gz with size 302kb. The corresponding postcript file has gzipped size 146kb. Submitted from: mendelma(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.1697 or http://arXiv.org/abs/0803.1697 or by email in unzipped form by transmitting an empty message with subject line uget 0803.1697 or in gzipped form by using subject line get 0803.1697 to: math(a)arXiv.org.

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Workshop in Analysis and Probability
by Dale Alspach 11 Mar '08

11 Mar '08

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2008 The Summer 2008 session of the Workshop in Analysis and Probability at Texas A&M University will be in session from July 7 until August 10. 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 8-10. Julien Giol <giol(a)math.tamu.edu>, David Kerr (chair) <kerr(a)math.tamu.edu>, and Andrew Toms <atoms(a)mathstat.yorku.ca> are organizing a Concentration Week on "Operator Algebras, Dynamics, and Classification" which will take place August 4-8. For more information, go to http://www.math.tamu.edu/~kerr/concweek08.html. Ron Douglas <rdouglas(a)math.tamu.edu> is organizing a Concentration Week on "Multivariate Operator Theory" that will take place July 28 - August 1. 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 "Operator Algebras, Dynamics, and Classification" contact David Kerr <kerr(a)math.tamu.edu>. For information about the Concentration Week on "Multivariate Operator Theory", contact Ron Douglas <rdouglas(a)math.tamu.edu>.

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Abstract of a paper by K. J. Swanepoel
by alspach＠fourier.math.okstate.edu 05 Mar '08

05 Mar '08

This is an announcement for the paper "Vertex degrees of Steiner minimal trees in $\ell_p^d$ and other smooth Minkowski spaces" by K. J. Swanepoel. Abstract: We find upper bounds for the degrees of vertices and Steiner points in Steiner Minimal Trees in the d-dimensional Banach spaces \ell_p^d independent of d. This is in contrast to Minimal Spanning Trees, where the maximum degree of vertices grows exponentially in d (Robins and Salowe, 1995). Our upper bounds follow from characterizations of singularities of SMT's due to Lawlor and Morgan (1994), which we extend, and certain \ell_p-inequalities. We derive a general upper bound of d+1 for the degree of vertices of an SMT in an arbitrary smooth d-dimensional Banach space; the same upper bound for Steiner points having been found by Lawlor and Morgan. We obtain a second upper bound for the degrees of vertices in terms of 1-summing norms. Archive classification: math.MG math.FA Mathematics Subject Classification: 05C05 (Primary); 49Q10 (Secondary) Citation: Discrete & Computational Geometry 21 (1999) 437-447 Remarks: 12 pages The source file(s), steiner-lp.tex: 30143 bytes, is(are) stored in gzipped form as 0803.0443.gz with size 10kb. The corresponding postcript file has gzipped size 81kb. Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0443 or http://arXiv.org/abs/0803.0443 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0443 or in gzipped form by using subject line get 0803.0443 to: math(a)arXiv.org.

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Abstract of a paper by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk
by alspach＠fourier.math.okstate.edu 05 Mar '08

05 Mar '08

This is an announcement for the paper "The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball" by Marcin Pilipczuk, Jakub Onufry Wojtaszczyk. Abstract: Random variables equidistributed on convex bodies have received quite a lot of attention in the last few years. In this paper we prove the negative association property (which generalizes the subindependence of coordinate slabs) for generalized Orlicz balls. This allows us to give a strong concentration property, along with a few moment comparison inequalities. Also, the theory of negatively associated variables is being developed in its own right, which allows us to hope more results will be available. Moreover, a simpler proof of a more general result for $\ell_p^n$ balls is given. Archive classification: math.PR math.FA Mathematics Subject Classification: 52A20, 60D05 Remarks: 44 pages (sorry) The source file(s), dlaorlic.tex: 166228 bytes, is(are) stored in gzipped form as 0803.0434.gz with size 46kb. The corresponding postcript file has gzipped size 253kb. Submitted from: onufryw(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0434 or http://arXiv.org/abs/0803.0434 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0434 or in gzipped form by using subject line get 0803.0434 to: math(a)arXiv.org.

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Abstract of a paper by Jakub Onufry Wojtaszczyk
by alspach＠fourier.math.okstate.edu 05 Mar '08

05 Mar '08

This is an announcement for the paper "The square negative correlation property for generalized Orlicz balls" by Jakub Onufry Wojtaszczyk. Abstract: Antilla, Ball and Perissinaki proved that the squares of coordinate functions in $\ell_p^n$ are negatively correlated. This paper extends their results to balls in generalized Orlicz norms on R^n. From this, the concentration of the Euclidean norm and a form of the Central Limit Theorem for the generalized Orlicz balls is deduced. Also, a counterexample for the square negative correlation hypothesis for 1-symmetric bodies is given. Currently the CLT is known in full generality for convex bodies (see the paper "Power-law estimates for the central limit theorem for convex sets" by B. Klartag), while for generalized Orlicz balls a much more general result is true (see "The negative association property for the absolute values of random variables equidistributed on a generalized Orlicz ball" by M. Pilipczuk and J. O. Wojtaszczyk). While, however, both aforementioned papers are rather long, complicated and technical, this paper gives a simple and elementary proof of, eg., the Euclidean concentration for generalized Orlicz balls. Archive classification: math.PR math.FA Mathematics Subject Classification: 52A20, 60D05 Citation: Geometric Aspects of Functional Analysis, Israel Seminar, The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0433 or http://arXiv.org/abs/0803.0433 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0433 or in gzipped form by using subject line get 0803.0433 to: math(a)arXiv.org.

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Abstract of a paper by Jakub Onufry Wojtaszczyk
by alspach＠fourier.math.okstate.edu 05 Mar '08

05 Mar '08

This is an announcement for the paper "A series whose sum range is an arbitrary finite set" by Jakub Onufry Wojtaszczyk. Abstract: In finitely-dimensional spaces the sum range of a series has to be an affine subspace. It is long known this is not the case in infinitely dimensional Banach spaces. In particular in 1984 M.I. Kadets and K. Wo\`{z}niakowski obtained an example of a series the sum range of which consisted of two points, and asked whether it is possible to obtain more than two, but finitely many points. This paper answers the question positively, by showing how to obtain an arbitrary finite set as the sum range of a series in any infinitely dimensional Banach space. Archive classification: math.FA Mathematics Subject Classification: 46B15 Citation: Studia Mathematica 171 (3) (2005), pp. 261-281 Remarks: 21 pages The source file(s), npunktow.tex: 64310 bytes, is(are) stored in gzipped form as 0803.0415.gz with size 20kb. The corresponding postcript file has gzipped size 127kb. Submitted from: onufryw(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0803.0415 or http://arXiv.org/abs/0803.0415 or by email in unzipped form by transmitting an empty message with subject line uget 0803.0415 or in gzipped form by using subject line get 0803.0415 to: math(a)arXiv.org.

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Banach March 2008