- Banach - mathdept.okstate.edu

Abstract of a paper by Tepper L Gill, Francis Mensah and Woodford W. Zachary
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "Adjoint operators on Banach spaces" by Tepper L Gill, Francis Mensah and Woodford W. Zachary. Abstract: In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results are new even for Hilbert spaces.) Our first two applications provide an extension of the Poincar\'{e} inequality and the Stone-von Neumann version of the spectral theorem for a large class of $C_0$-generators of contraction semigroups on separable Banach spaces. Our third application provides a natural extension of the Schatten-class of operators to all separable Banach spaces. As a part of this program, we introduce a new class of separable Banach spaces. As a side benefit, these spaces also provide a natural framework for the (rigorous) construction of the path integral as envisioned by Feynman. Archive classification: math-ph math.FA math.MP Mathematics Subject Classification: 46B03, 47D03, 47H06, 47F05, 35Q80 Submitted from: tgill(a)howard.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.4922 or http://arXiv.org/abs/1010.4922

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Abstract of a paper by Isaac Goldbring
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "Definable operators on Hilbert spaces" by Isaac Goldbring. Abstract: Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators. Archive classification: math.LO math.FA Remarks: 10 pages Submitted from: isaac(a)math.ucla.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.2243 or http://arXiv.org/abs/1010.2243

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Abstract of a paper by Robert Cauty
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "Points fixes des applications compactes dans les espaces ULC" by Robert Cauty. Abstract: A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$, $\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for $(x,y)\in U$ and $(x,t)\in X\times[0,1]$. This class contains all ANRs, all locally contractible topological groups and the open subsets of convex subsets of linear topological spaces. In a series of papers, we extended the fixed point theory of compact continuous maps, which was well developped for ANRs, to all separeted locally equiconnected spaces. This generalization includes a proof of Schauder's conjecture for compact maps of convex sets. This paper is a survey of that work. The generalization has two steps: the metrizable case, and the passage from the metrizable case to the general case. The metrizable case is, by far, the most difficult. To treat this case, we introduced in [4] the notion of algebraic ANR. Since the proof that metrizable locally equiconnected spaces are algebraic ANRs is rather difficult, we give here a detaled sketch of it in the case of a compact convex subset of a metrizable t.v.s.. The passage from the metrizable case to the general case uses a free functor and representations of compact spaces as inverse limits of some special inverse systems of metrizable compacta. Archive classification: math.GN math.AT math.FA Mathematics Subject Classification: 54C55 Submitted from: cauty(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.2401 or http://arXiv.org/abs/1010.2401

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Abstract of a paper by Maxim V. Balashov and Dusan Repovs
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "Polyhedral approximations of strictly convex compacta" by Maxim V. Balashov and Dusan Repovs. Abstract: We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the Hausdorff metric. We also obtain new estimates of an approximate algorithm for finding the convex hulls. Archive classification: math.FA math.GN math.MG Mathematics Subject Classification: 52A20, 52A27, 52A99, 52A41, 52B55 Citation: J. Math. Anal. Appl. 374:2 (2011), 529-537 Submitted from: dusan.repovs(a)guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.2320 or http://arXiv.org/abs/1010.2320

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Abstract of a paper by Volker Runde
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "A new and simple proof of Schauder's theorem" by Volker Runde. Abstract: Schauder's theorem asserts that a bounded linear operator between Banach spaces is compact if ad only if its adjoint is. We give a new proof of this result, which is both short and completely elementary in the sense that it does not depend on anything beyond basic functional analysis, i.e., the Hahn--Banach theorem and some of its consequences; in particular, we avoid the Arzela--Ascoli theorem (and any kind of related diagonal argument). Archive classification: math.FA Submitted from: vrunde(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.1298 or http://arXiv.org/abs/1010.1298

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Abstract of a paper by Vegard Lima and N. Lovasoa Randrianarivony
by alspach＠fourier.math.okstate.edu 29 Oct '10

29 Oct '10

This is an announcement for the paper "Property $(\beta)$ and uniform quotient maps" by Vegard Lima and N. Lovasoa Randrianarivony. Abstract: In 1999, Bates, Johnson, Lindenstrauss, Preiss and Schechtman asked whether a Banach space that is a uniform quotient of $\ell_p$, $1 < p \neq 2 < \infty$, must be isomorphic to a linear quotient of $\ell_p$. We apply the geometric property $(\beta)$ of Rolewicz to the study of uniform and Lipschitz quotient maps, and answer the above question positively for the case $1<p<2$. We also give a necessary condition for a Banach space to have $c_0$ as a uniform quotient. Archive classification: math.FA math.MG Submitted from: nrandria(a)slu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1010.0184 or http://arXiv.org/abs/1010.0184

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J J Jerry Uhl passed away
by Elias Saab 24 Oct '10

24 Oct '10

---------- Forwarded message ---------- From: Debra Woods <dwoods2(a)illinois.edu> Date: Sun, Oct 24, 2010 at 9:21 AM Subject: Fwd: J Jerry Uhl To: "jerryfriends(a)cm.math.uiuc.edu" <jerryfriends(a)cm.math.uiuc.edu> Hello all, I wanted to let you all know that Jerry passed away last night in his sleep. I'll send more information as I find it out. Debra Begin forwarded message: *From: *"Mr. Jac M Knoop" <jac(a)amsincorporated.net> *Date: *October 24, 2010 8:33:37 AM CDT *To: *Debra Woods <dwoods(a)cm.math.uiuc.edu>, Deborah Hughes Hallett < deborah_hughes_hallett(a)harvard.edu>, Suzanne Smith <suzannesmith(a)hughes.net>, Bill Davis <nudge_1994(a)yahoo.com>, Mr&Mrs Bill & Mary Davis < bigdogmom1960(a)yahoo.com>, Linda Krukewitt <krukfarms(a)yahoo.com> *Subject: **J Jerry Uhl* Dear Friends, This morning our friend and neighbor, John Jerry Uhl, passed away in his sleep. Everything looked very peaceful. No details of the funeral or cremation are available at this time, Jerry's sister is on her way to Illinois and we will have more information later. *Sincerely,* Jac M Knoop AMS Incorporated Manufacturers Representatives and Distributors "The work will wait while you show a child the rainbow, but the rainbow won't wait while you finish the work." -- 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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for the BBB
by Gilles Godefroy 22 Oct '10

22 Oct '10

Nigel Kalton passed away on 31 August, 2010. He had work in progress and the information available so far leaves it unclear whether some articles, which were found on his desk in apparently final form, have been submitted or not. The titles are: - Hermitian operators on complex Banach lattices and a problem of Garth Dales. - Uniform homeomorphisms of Banach spaces and asymptotic structure. - Examples of uniformly homeomorphic Banach spaces. - The uniform structure of Banach spaces. We would be grateful for any information on the status of these papers, which will be submitted in Nigel's name if needed. Please kindly write to casazzap(a)missouri.edu and to godefroy(a)math.jussieu.fr if you know something. Your help is appreciated.

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Abstract of a paper by Daniel Pellegrino and Joedson Santos
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "Abstract ideals of absolutely summing multilinear operators" by Daniel Pellegrino and Joedson Santos. Abstract: This paper has a twofold purpose: to present an overview of the different multi-ideals that generalize the concept of absolutely summing operators and to sketch the beginning of a research project related to an objective search of \textquotedblleft perfect\textquotedblright\ multilinear extensions of the ideal of absolutely summing operators. The final section contains some open problems that may indicate lines for future investigation. Archive classification: math.FA Remarks: 10 pages Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.4807 or http://arXiv.org/abs/1009.4807

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Abstract of a paper by Andrea Marchese and Clemente Zanco
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "On a question by Corson about point-finite coverings" by Andrea Marchese and Clemente Zanco. Abstract: We answer in the affirmative the following question raised by H. H. Corson in 1961: "Is it possible to cover every Banach space X by bounded convex sets with nonempty interior in such a way that no point of X belongs to infinitely many of them?" Actually we show the way to produce in every Banach space X a bounded convex tiling of order 2, i.e. a covering of X by bounded convex closed sets with nonempty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles. Archive classification: math.FA Remarks: to appear on Israel J. Math Submitted from: marchese(a)mail.dm.unipi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.4681 or http://arXiv.org/abs/1009.4681

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