December 2005 - Banach - mathdept.okstate.edu

Interpolation Theory and Applications: A Conference in Honor of Michael Cwikel
by Mario M. Milman 21 Dec '05

21 Dec '05

Interpolation Theory and Applications: A Conference in Honor of Michael Cwikel More information: http://www.ams.org/mathcal/info/2006_mar29-31_coralgables.html

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Nicole Tomczak-Jaegerman: Recipient of the 2006 CRM-Fields-PIMS Prize
by Dale Alspach 20 Dec '05

20 Dec '05

(From PIMS) NICOLE TOMCZAK-JAEGERMAN: RECIPIENT OF THE 2006 CRM-FIELDS-PIMS PRIZE The directors of the Centre de recherches mathematiques (CRM) of l'Universite de Montreal - Francois Lalonde, the Fields Institute - Barbara Keyfitz, and the Pacific Institute for the Mathematical Sciences - Ivar Ekeland, are pleased to announce the awarding of the CRM-Fields-PIMS Prize for 2006 to Professor Nicole Tomczak-Jaegermann of the University of Alberta in recognition of her exceptional achievements in functional analysis and geometric analysis. The prize was established in 1994 as the CRM-Fields prize to recognize exceptional research in the mathematical sciences. In 2005, PIMS became an equal partner and the name was changed to the CRM-Fields-PIMS prize. A committee appointed by the three institutes chooses the recipient. Nicole Tomczak-Jaegermann, this year's recipient, is one of the world's leading mathematicians working in functional analysis. She has made outstanding contributions to infinite dimensional Banach space theory, asymptotic geometric analysis, and the interaction between these two streams of modern functional analysis. She holds a Canada Research Chair in Geometric Analysis at the University of Alberta. In 1998 she gave an invited lecture at the International Congress of Mathematicians, is a Fellow of the Royal Society of Canada, received a Killam Research Fellowship, and the Krieger-Nelson Prize Lectureship of the Canadian Mathematical Society. Previous recipients of the prize are H.S.M. (Donald) Coxeter, George A. Elliott, James Arthur, Robert V. Moody, Stephen A. Cook, Israel Michael Sigal, William T. Tutte, John B. Friedlander, John McKay, Edwin Perkins, Donald A. Dawson, and David Boyd. For more information please see http://www.pims.math.ca

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Abstract of a paper by Catalin Badea and Vladimir Mueller
by Dale Alspach 15 Dec '05

15 Dec '05

This is an announcement for the paper "Growth conditions and inverse producing extensions" by Catalin Badea and Vladimir Mueller. Abstract: We study the invertibility of Banach algebras elements in their extensions, and invertible extensions of Banach and Hilbert space operators with prescribed growth conditions for the norm of inverses. As applications, the solutions of two open problems are obtained. In the first one we give a characterization of E(T)-subscalar operators in terms of growth conditions. In the second one we show that operators satisfying a Beurling-type growth condition possess Bishop's property beta. Other applications are also given. Archive classification: Functional Analysis; Operator Algebras Remarks: 22 pages The source file(s), bm1arx.tex: 60879 bytes, is(are) stored in gzipped form as 0512321.gz with size 19kb. The corresponding postcript file has gzipped size 90kb. Submitted from: catalin.badea(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0512321 or http://arXiv.org/abs/math.FA/0512321 or by email in unzipped form by transmitting an empty message with subject line uget 0512321 or in gzipped form by using subject line get 0512321 to: math(a)arXiv.org.

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Abstract of a paper by Assaf Naor and Gideon Schechtman
by Dale Alspach 14 Dec '05

14 Dec '05

This is an announcement for the paper "Planar earthmover is not in $L_1$" by Assaf Naor and Gideon Schechtman. Abstract: We show that any $L_1$ embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid $\{0,1,...,n\}^2\subseteq \R^2$ incurs distortion $\Omega(\sqrt{\log n})$. We also use Fourier analytic techniques to construct a simple $L_1$ embedding of this space which has distortion $O(\log n)$. Archive classification: Computational Geometry; Functional Analysis The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: anaor(a)microsoft.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/cs.CG/0509074 or http://arXiv.org/abs/cs.CG/0509074 or by email in unzipped form by transmitting an empty message with subject line uget 09074 or in gzipped form by using subject line get 09074 to: math(a)arXiv.org.

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Abstract of a paper by Emanuel Milman
by Dale Alspach 13 Dec '05

13 Dec '05

This is an announcement for the paper "A comment on the low-dimensional Busemann-Petty problem" by Emanuel Milman. Abstract: The generalized Busemann-Petty problem asks whether centrally-symmetric convex bodies having larger volume of all m-dimensional sections necessarily have larger volume. When m>3 this is known to be false, but the cases m=2,3 are still open. In those cases, it is shown that when the smaller body's radial function is a (n-m)-th root of the radial function of a convex body, the answer to the generalized Busemann-Petty problem is positive (for any larger star-body). Several immediate corollaries of this observation are also discussed. Archive classification: Functional Analysis; Metric Geometry Remarks: 9 pages, to appear in GAFA Seminar Notes The source file(s), low-dim-BP-problem.bbl: 4623 bytes, low-dim-BP-problem.tex: 24305 bytes, is(are) stored in gzipped form as 0512208.tar.gz with size 10kb. The corresponding postcript file has gzipped size 53kb. 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/0512208 or http://arXiv.org/abs/math.FA/0512208 or by email in unzipped form by transmitting an empty message with subject line uget 0512208 or in gzipped form by using subject line get 0512208 to: math(a)arXiv.org.

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Abstract of a paper by Emanuel Milman
by Dale Alspach 13 Dec '05

13 Dec '05

This is an announcement for the paper "Dual mixed volumes and the slicing problem" by Emanuel Milman. Abstract: We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of L_p and related spaces. An extension of these results to negative values of p is also obtained, using generalized intersection-bodies. In particular, we show that the isotropic constant of a convex body which is contained in an intersection-body is bounded (up to a constant) by the ratio between the latter's mean-radius and the former's volume-radius. We also show how type or cotype 2 may be used to easily prove inequalities on any isotropic measure. Archive classification: Functional Analysis; Metric Geometry Remarks: 38 pages, to appear in Advance in Mathematics The source file(s), dual-mixed-volumes-and-slicing-problem-for-arxiv.bbl: 7985 bytes, dual-mixed-volumes-and-slicing-problem-for-arxiv.tex: 94404 bytes, is(are) stored in gzipped form as 0512207.tar.gz with size 29kb. The corresponding postcript file has gzipped size 130kb. 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/0512207 or http://arXiv.org/abs/math.FA/0512207 or by email in unzipped form by transmitting an empty message with subject line uget 0512207 or in gzipped form by using subject line get 0512207 to: math(a)arXiv.org.

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CBMS conference on A Probabalistic and Combinatorial Approach in Analysis
by zvavitch＠math.kent.edu 07 Dec '05

07 Dec '05

Dear Friends, In August 2006 (from the 6th to the 13th, to be precise), the Department of Mathematical Science of Kent State University will be hosting a CBMS conference, 'A Probabilistic and Combinatorial Approach in Analysis', with Professor Mark Rudelson from the University of Missouri as the main speaker. We hope that you will be able to participate. With CBMS funding we will be able to cover local expenses for a limited number of participants, so it is advisable to reply as soon as possible to Artem Zvavitch (zvavitch(a)math.kent.edu) At this time, we have very limited funding for travel; to be as efficient as possible in the use of the available travel funds, we encourage you to encourage your graduate students and postdocs to participate, as well. For further information and breaking news a look at http://www.math.kent.edu/math/CBMS.cfm is advised. Please note that your early response will help us gauge the needs for housing, lecture room(s), etc. We hope to be sending out information regarding housing by the end of December. HOPE TO SEE YOU IN KENT NEXT AUGUST!! Best Regards, Richard Aron, Joe Diestel, Per Enflo, Victor Lomonosov, Andrew Tonge, and Artem Zvavitch

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Abstract of a paper by Emanuel Milman
by Dale Alspach 05 Dec '05

05 Dec '05

This is an announcement for the paper "Generalized intersection bodies" by Emanuel Milman. Abstract: We study the structures of two types of generalizations of intersection-bodies and the problem of whether they are in fact equivalent. Intersection-bodies were introduced by Lutwak and played a key role in the solution of the Busemann-Petty problem. A natural geometric generalization of this problem considered by Zhang, led him to introduce one type of generalized intersection-bodies. A second type was introduced by Koldobsky, who studied a different analytic generalization of this problem. Koldobsky also studied the connection between these two types of bodies, and noted that an equivalence between these two notions would completely settle the unresolved cases in the generalized Busemann-Petty problem. We show that these classes share many identical structure properties, proving the same results using Integral Geometry techniques for Zhang's class and Fourier transform techniques for Koldobsky's class. Using a Functional Analytic approach, we give several surprising equivalent formulations for the equivalence problem, which reveal a deep connection to several fundamental problems in the Integral Geometry of the Grassmann Manifold. Archive classification: Functional Analysis; Geometric Topology; Metric Geometry Remarks: 44 pages The source file(s), generalized-intersection-bodies-for-arxiv.bbl: 6010 bytes, generalized-intersection-bodies-for-arxiv.tex: 129282 bytes, is(are) stored in gzipped form as 0512058.tar.gz with size 38kb. The corresponding postcript file has gzipped size 159kb. 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/0512058 or http://arXiv.org/abs/math.FA/0512058 or by email in unzipped form by transmitting an empty message with subject line uget 0512058 or in gzipped form by using subject line get 0512058 to: math(a)arXiv.org.

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Abstract of a paper by Manor Mendel and Assaf Naor
by Dale Alspach 05 Dec '05

05 Dec '05

This is an announcement for the paper "Ramsey partitions and proximity data structures" by Manor Mendel and Assaf Naor. Abstract: This paper addresses two problems lying at the intersection of geometric analysis and theoretical computer science: The non-linear isomorphic Dvoretzky theorem and the design of good approximate distance oracles for large distortion. We introduce the notion of Ramsey partitions of a finite metric space, and show that the existence of good Ramsey partitions implies a solution to the metric Ramsey problem for large distortion (a.k.a. the non-linear version of the isomorphic Dvoretzky theorem, as introduced by Bourgain, Figiel, and Milman in \cite{BFM86}). We then proceed to construct optimal Ramsey partitions, and use them to show that for every $\e\in (0,1)$, any $n$-point metric space has a subset of size $n^{1-\e}$ which embeds into Hilbert space with distortion $O(1/\e)$. This result is best possible and improves part of the metric Ramsey theorem of Bartal, Linial, Mendel and Naor \cite{BLMN05}, in addition to considerably simplifying its proof. We use our new Ramsey partitions to design the best known approximate distance oracles when the distortion is large, closing a gap left open by Thorup and Zwick in \cite{TZ05}. Namely, we show that for any $n$ point metric space $X$, and $k\geq 1$, there exists an $O(k)$-approximate distance oracle whose storage requirement is $O(n^{1+1/k})$, and whose query time is a universal constant. We also discuss applications of Ramsey partitions to various other geometric data structure problems, such as the design of efficient data structures for approximate ranking. Archive classification: Data Structures and Algorithms; Computational Geometry; Metric Geometry; Functional Analysis The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: anaor(a)microsoft.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/cs.DS/0511084 or http://arXiv.org/abs/cs.DS/0511084 or by email in unzipped form by transmitting an empty message with subject line uget 11084 or in gzipped form by using subject line get 11084 to: math(a)arXiv.org.

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Abstract of a paper by Jakub Duda
by Dale Alspach 05 Dec '05

05 Dec '05

This is an announcement for the paper "On Gateaux differentiability of pointwise Lipschitz mappings" by Jakub Duda. Abstract: We prove that for every function $f:X\to Y$, where $X$ is a separable Banach space and $Y$ is a Banach space with RNP, there exists a set $A\in\tilde\mcA$ such that $f$ is Gateaux differentiable at all $x\in S(f)\setminus A$, where $S(f)$ is the set of points where $f$ is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every $K$-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to $\tilde\mcC$; this improves a result due to Borwein and Wang. Another corollary is that if $X$ is Asplund, $f:X\to\R$ cone monotone, $g:X\to\R$ continuous convex, then there exists a point in $X$, where $f$ is Hadamard differentiable and $g$ is Frechet differentiable. Archive classification: Functional Analysis Mathematics Subject Classification: 46G05; 46T20 Remarks: 11 pages; added name The source file(s), stronger_stepanoff.tex: 48652 bytes, is(are) stored in gzipped form as 0511565.gz with size 15kb. The corresponding postcript file has gzipped size 61kb. Submitted from: jakub.duda(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0511565 or http://arXiv.org/abs/math.FA/0511565 or by email in unzipped form by transmitting an empty message with subject line uget 0511565 or in gzipped form by using subject line get 0511565 to: math(a)arXiv.org.

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