Banach October 2014

banach@mathdept.okstate.edu

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15 discussions

Abstract of a paper by Sun Kwang Kim, Han Ju Lee, and Miguel Martin
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Bishop-Phelps-Bollob\'as property for bilinear forms on spaces of continuous functions" by Sun Kwang Kim, Han Ju Lee, and Miguel Martin. Abstract: It is shown that the Bishop-Phelps-Bollob\'as theorem holds for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary locally compact topological Hausdorff spaces $L_1$ and $L_2$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22 Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.0514 or http://arXiv.org/abs/1410.0514

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Abstract of a paper by Mark Rudelson
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "On the complexity of the set of unconditional convex bodies" by Mark Rudelson. Abstract: We show that for any t>1, the set of unconditional convex bodies in R^n contains a t-separated subset of cardinality at least 0.1 exp exp (C(t) n). This implies that there exists an unconditional convex body in R^n which cannot be approximated within the distance d by a projection of a polytope with N faces unless N > exp(c(d)n). We also show that for t>2, the cardinality of a t-separated set of completely symmetric bodies in R^n does not exceed exp exp (c(t)(log n)^2). Archive classification: math.MG math.FA Remarks: 17 pages Submitted from: rudelson(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1410.0092 or http://arXiv.org/abs/1410.0092

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Abstract of a paper by Michael Demuth, Franz Hanauska, Marcel Hansmann, and Guy Katriel
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Estimating the number of eigenvalues of linear operators on Banach spaces" by Michael Demuth, Franz Hanauska, Marcel Hansmann, and Guy Katriel. Abstract: Let $L_0$ be a bounded operator on a Banach space, and consider a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned with obtaining bounds on the number of eigenvalues of $L$ in subsets of the complement of the essential spectrum of $L_0$, in terms of the approximation numbers of the perturbing operator $K$. Our results can be considered as wide generalizations of classical results on the distribution of eigenvalues of compact operators, which correspond to the case $L_0=0$. They also extend previous results on operators in Hilbert space. Our method employs complex analysis and a new finite-dimensional reduction, allowing us to avoid using the existing theory of determinants in Banach spaces, which would require strong restrictions on $K$. Several open questions regarding the sharpness of our results are raised, and an example is constructed showing that there are some essential differences in the possible distribution of eigenvalues of operators in general Banach spaces, compared to the Hilbert space case. Archive classification: math.SP math.FA Submitted from: marcel.hansmann(a)mathematik.tu-chemnitz.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.8569 or http://arXiv.org/abs/1409.8569

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Abstract of a paper by Niels Jakob Laustsen and Richard Skillicorn
by alspach＠math.okstate.edu 21 Oct '14

21 Oct '14

This is an announcement for the paper "Splittings of extensions of the algebra of bounded operators on a space" by Niels Jakob Laustsen and Richard Skillicorn. Abstract: We show that there exist a Banach space E, a unital Banach algebra A with Jacobson radical rad A, and a continuous, surjective algebra homomorphism f from A onto the Banach algebra B(E) of bounded operators on E such that ker f = rad A and the corresponding extension {0} -> rad A -> A -> B(E) -> {0} is singular (in the sense that rad A has trivial multiplication) and splits algebraically, but it does not split strongly. This conclusion complements the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999). The Banach space E that we use is a quotient of the l_2-direct sum of an infinite sequence of James-type quasi-reflexive Banach spaces; it was originally introduced by Read (J. London Math. Soc. 1989). Archive classification: math.FA Submitted from: r.skillicorn(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.8203 or http://arXiv.org/abs/1409.8203

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Announcement of a special issue of Annals of Functional Analysis
by Dale Alspach 12 Oct '14

12 Oct '14

Dear *Colleague*, I would like to inform you that a special issue (2016) of the *Annals of Functional Analysis (AFA) is dedicated to* *Professor *Anthony To-Ming* Lau* for his significant contributions to several areas of Functional Analysis, Abstract Harmonic Analysis and Operator Theory. The journal particularly invites articles related to works of *A. T.-M. Lau*, but other papers within the scope of the journal (MSC43, MSC46 and MSC47) are warmly welcomed. The usual reviewing procedures and standards of AFA will be applied to all papers for the special issue. *Preliminary papers or summaries of results previously published are not acceptable.* ** %%%%%%%%%%%%%%%%%%%%%%%%%%%%% *Submission should be done via the online submission of AFA at:* *http://www.emis.de/journals/AFA/* The deadline for submission is: *** 30 March 2015 *** %%%%%%%%%%%%%%%%%%%%%%%%%%%%% Please let the editor-in-chief know whether you are potentially able to have a contribution to this issue or not (and give an approximate date for receiving your paper, if possible). Best wishes, *M. S. Moslehian * Editor-in-chief* * http://www.um.ac.ir/~moslehian/ <http://www.um.ac.ir/%7Emoslehian/>

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Banach October 2014