Banach

banach@mathdept.okstate.edu

2549 discussions

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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Abstract of a paper by Y. Gordon, M. Junge, M. Meyer and S. Reisner
by alspach＠fourier.math.okstate.edu 19 Aug '10

19 Aug '10

This is an announcement for the paper "The GL-l.u.st. constant and asymmetry of the Kalton-Peck twisted sum in finite dimensions" by Y. Gordon, M. Junge, M. Meyer and S. Reisner. Abstract: We prove that the Kalton-Peck twisted sum $Z_2^n$ of $n$-dimensional Hilbert spaces has GL-l.u.st.\ constant of order $\log n$ and bounded GL constant. This is the first concrete example which shows different explicit orders of growth in the GL and GL-l.u.st.\ constants. We discuss also the asymmetry constants of $Z_2^n$. Archive classification: math.FA Remarks: Proc. AMS, accepted Submitted from: reisner(a)math.haifa.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.4692 or http://arXiv.org/abs/1007.4692

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SUMIRFAS schedule
by Dale Alspach 22 Jul '10

22 Jul '10

Attachments are not normally allowed on messages to Banach. They are removed and stored on the server. The SUMIRFAS schedule that Bill Johnson sent out is available for viewing at http://cauchy.math.okstate.edu/pipermail/banach/attachments/20100721/6d4220… Dale Alspach

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SUMIRFAS schedule
by Bill Johnson 21 Jul '10

21 Jul '10

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Abstract of a paper by Qi Lu, Jiongmin Yong and Xu Zhang
by alspach＠fourier.math.okstate.edu 20 Jul '10

20 Jul '10

This is an announcement for the paper "Representation of Ito integrals by Lebesgue/Bochner integrals" by Qi Lu, Jiongmin Yong and Xu Zhang. Abstract: In [22], it was proved that as long as the integrand has certain properties, the corresponding It\^o integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later can be regarded as a variant of the classical Riesz Representation Theorem, and therefore it will be useful in studying other problems. Some remarkable consequences are presented as well, including a reasonable definition of exact controllability for stochastic differential equations and a condition which implies a Black-Scholes market to be complete. Archive classification: math.PR math.FA math.OC Remarks: 26pages Submitted from: xuzhang(a)amss.ac.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1007.2969 or http://arXiv.org/abs/1007.2969

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