September 2010 - Banach - mathdept.okstate.edu

Abstract of a paper by V.L. Dolnikov and R.N. Karasev
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Dvoretzky type theorems for multivariate polynomials and sections of convex bodies" by V.L. Dolnikov and R.N. Karasev. Abstract: In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. The latter conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture. Archive classification: math.MG math.AT math.CO math.FA Mathematics Subject Classification: 46B20, 05D10, 26C10, 52A21, 52A23, 55M35 Submitted from: r_n_karasev(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.0392 or http://arXiv.org/abs/1009.0392

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Meeting: Integration, Vector Measures and Related Topics IV'' Dedicated to Joe Diestel. Murcia 2011
by IntMedVec Murcia 2011 17 Sep '10

17 Sep '10

Meeting: Integration, Vector Measures and Related Topics IV'' Dedicated to Joe Diestel. University of Murcia, Murcia, Spain March 2 - March 5, 2011 Description: The aim of this four day conference is to bring together experienced and novice researchers interested in Integration, Vector Measures and their Applications. The conference will feature a series of plenary and short lectures as well as a mini-course and contributed posters on recent advances in the subject. The previous meetings of this series of conferences were held in Valencia in 2004, Sevilla in 2006 and Eichstätt in 2008. Partial support for a small number of participants is expected to be available. Recent recipients of doctoral degrees and pre-doc students are encouraged to apply. The meeting will take place in La Manga del Mar Menor, Murcia, from March 2? March 5, 2011 (both days included). It will be organized by the Functional Analysis Group of the University of Murcia. Information: http://www.um.es/beca/Murcia2011/index.php Sponsors: UMU, MCIN, iMath Consolider, Fundacion Seneca CARM On behalf of the organizers. Integration, Vector Measures and Related Topics IV. Murcia. March 2-5. 2011 http://www.um.es/beca/Murcia2011/index.php

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Abstract of a paper by Mohammad Sal Moslehian and John M. Rassias
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "A characterization of inner product spaces" by Mohammad Sal Moslehian and John M. Rassias. Abstract: In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X, \|\cdot\|)$ is an inner product space if $$\sum_{\varepsilon_i \in \{-1,1\}} \left\|x_1 + \sum_{i=2}^k\varepsilon_ix_i\right\|^2=\sum_{\varepsilon_i \in \{-1,1\}} \left(\|x_1\| + \sum_{i=2}^k\varepsilon_i\|x_i\|\right)^2\,,$$ for some positive integer $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Conversely, if $(X, \|\cdot\|)$ is an inner product space, then the equality above holds for all $k\geq 2$ and all $x_1, \ldots, x_k \in X$. Archive classification: math.FA math.CA Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05 Remarks: 8 Pages, to appear in Kochi J. Math. (Japan) Submitted from: moslehian(a)ferdowsi.um.ac.ir The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.0079 or http://arXiv.org/abs/1009.0079

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Abstract of a paper by Iosif Pinelis
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "On the von Bahr--Esseen inequality" by Iosif Pinelis. Abstract: The well-known von Bahr--Esseen bound on the absolute pth moments of martingales with p in (1,2] is extended to a large class of moment functions, and now with a best possible constant factor (which depends on the moment function). As an application, measure concentration inequalities for separately Lipschitz functions on product spaces are obtained. Relations with p-uniformly smooth and q-uniformly convex normed spaces are discussed. Archive classification: math.PR math.FA Mathematics Subject Classification: Primary 60E15, 60B11, 62G10, secondary 46B09, 46B20, 46B10 Submitted from: ipinelis(a)mtu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.5350 or http://arXiv.org/abs/1008.5350

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Abstract of a paper by Nikos Yannakakis
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "Stampacchia's property, self-duality and orthogonality relations" by Nikos Yannakakis. Abstract: We show that if the conclusion of the well known Stampacchia Theorem, on variational inequalities, holds on a Banach space X, then X is isomorphic to a Hilbert space. Motivated by this we obtain a relevant result concerning self-dual Banach spaces and investigate some connections between existing notions of orthogonality and self-duality. Moreover, we revisit the notion of the cosine of a linear operator and show that it can be used to characterize Hilbert space structure. Finally, we present some consequences of our results to quadratic forms and to evolution triples. Archive classification: math.FA Submitted from: nyian(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.4958 or http://arXiv.org/abs/1008.4958

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Abstract of a paper by Luis Rademacher
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "On the monotonicity of the expected volume of a random simplex" by Luis Rademacher. Abstract: Let a random simplex in a d-dimensional convex body be the convex hull of d+1 random points from the body. We study the following question: As a function of the convex body, is the expected volume of a random simplex monotone non-decreasing under inclusion? We show that this holds if d is 1 or 2, and does not hold if d >= 4. We also prove similar results for higher moments of the volume of a random simplex, in particular for the second moment, which corresponds to the determinant of the covariance matrix of the convex body. These questions are motivated by the slicing conjecture. Archive classification: math.PR math.FA math.MG Submitted from: lrademac(a)cse.ohio-state.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.3944 or http://arXiv.org/abs/1008.3944

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Abstract of a paper by Tanja Eisner and Tamas Matrai
by alspach＠fourier.math.okstate.edu 08 Sep '10

08 Sep '10

This is an announcement for the paper "On typical properties of Hilbert space operators" by Tanja Eisner and Tamas Matrai. Abstract: We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C_0-semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators. Archive classification: math.FA math.GN Mathematics Subject Classification: 47A05, 47A10 (Primary) 54E52 (Secondary) Remarks: 22 pages, submitted Submitted from: talo(a)fa.uni-tuebingen.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1008.3326 or http://arXiv.org/abs/1008.3326

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Please Post This
by Casazza, Peter 07 Sep '10

07 Sep '10

Nigel J. Kalton of the University of Missouri passed away from a stroke on August 31, 2010. There will be a memorial service held at the Reynolds Alumni Center on the MU campus from 1-3 pm on Friday, October 1. The family has requested that in lieu of flowers, donations be made to the Nigel Kalton Memorial Scholarship. If you wish to contribute, please send a check to the address below made out to The University of Missouri with a notation that it is for the Nigel Kalton Scholarship. Nigel was a giant of a person and a mathematician. He will be sadly missed. Kimberly Dostoglou Department of Mathematics University of Missouri Columbia, MO 65211

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Memorial Service for Nigel Kalton
by Elias Saab 02 Sep '10

02 Sep '10

---------- Forwarded message ---------- From: Himmelberg, Glen R. <HimmelbergG(a)missouri.edu> Date: Wed, Sep 1, 2010 at 2:22 PM Subject: Memorial Service for Nigel Kalton To: MU A&S Math all <MUA&SMathall(a)missouri.edu <MUA%26SMathall(a)missouri.edu> > Dear All: The family of Nigel Kalton has scheduled a memorial service for Nigel on Friday, October 1, from 1:00 to 3:00 pm at Reynolds Alumni Center. There will be a service followed by a reception. Sincerely, Glen -- Glen R. Himmelberg Chair, Department of Mathematics University of Missouri Columbia, MO 65211 Phone: 573-882-6222 Fax: 573-882-1869 -- Elias Saab, Emeritus Professor Department of Mathematics 202 Math Science Building University of Missouri-Columbia Columbia, MO 65211 Phone (Office 308 MSB) 573-882-4530 e-mail eliassaab123(a)gmail.com http://saab.org

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Nigel Kalton Has Died
by elias 01 Sep '10

01 Sep '10

Hi All, My son called and said that Nigel's daughter told him that Nigel died. Nigel suffered a severe stroke a couple of days ago and did not recover. It is a devastating loss for all of us. Elias Elias Saab, Emeritus Professor Department of Mathematics 202 Math Science Building University of Missouri-Columbia Columbia, MO 65211 Phone (Office) 573-884-0621 e-mail elias(a)math.missouri.edu http://saab.org

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