Banach

banach@mathdept.okstate.edu

2549 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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Abstract of a paper by Kati Ain and Eve Oja
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "On $(p,r)$-null sequences and their relatives" by Kati Ain and Eve Oja. Abstract: Let $1\leq p < \infty$ and $1\leq r \leq p^\ast$, where $p^\ast$ is the conjugate index of $p$. We prove an omnibus theorem, which provides numerous equivalences for a sequence $(x_n)$ in a Banach space $X$ to be a $(p,r)$-null sequence. One of them is that $(x_n)$ is $(p,r)$-null if and only if $(x_n)$ is null and relatively $(p,r)$-compact. This equivalence is known in the ''limit'' case when $r=p^\ast$, the case of the $p$-null sequence and $p$-compactness. Our approach is more direct and easier than those applied for the proof of the latter result. We apply it also to characterize the unconditional and weak versions of $(p,r)$-null sequences. Archive classification: math.FA Submitted from: kati.ain(a)ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.6476 or http://arXiv.org/abs/1409.6476

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Abstract of a paper by Fernanda Botelho and James Jamison
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "Isometries and Hermitian operators on $\mathcal{B}_0(\triangle, E)$" by Fernanda Botelho and James Jamison. Abstract: In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho(a)memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5381 or http://arXiv.org/abs/1409.5381

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Abstract of a paper by Fernanda Botelho
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "Isometries and Hermitian operators on Zygmund spaces" by Fernanda Botelho. Abstract: In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded. Archive classification: math.FA Mathematics Subject Classification: 46E15, 47B15, 47B38 Submitted from: mbotelho(a)memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.5378 or http://arXiv.org/abs/1409.5378

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Abstract of a paper by Dimosthenis Drivaliaris and Nikos Yannakakis
by alspach＠math.okstate.edu 26 Sep '14

26 Sep '14

This is an announcement for the paper "The angle of an operator and range and kernel complementarity" by Dimosthenis Drivaliaris and Nikos Yannakakis. Abstract: We show that if the angle of a bounded linear operator on a Banach space with closed range is less than $\pi$, then its range and kernel are complementary. We also show that in finite dimensions and up to rotations this simple geometric property characterizes operators for which range and kernel are complementary. For operators on a Hilbert space we present a sufficient condition, involving the distance of the boundary of the numerical range from the origin, for the range and the kernel to be complementary. Archive classification: math.FA Mathematics Subject Classification: 47A05, 47A12, 47A10, 47B44, 46B20 Submitted from: d.drivaliaris(a)fme.aegean.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.4195 or http://arXiv.org/abs/1409.4195

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Abstract of a paper by Thomas Schlumprecht and Andras Zsak
by alspach＠math.okstate.edu 12 Sep '14

12 Sep '14

This is an announcement for the paper "The algebra of bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals" by Thomas Schlumprecht and Andras Zsak. Abstract: We prove that in the reflexive range $1<p<q<\infty$ the algebra of all bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals. This solves a problem raised by A. Pietsch in his book `Operator ideals'. Archive classification: math.FA Mathematics Subject Classification: 47L20, 46B25 Remarks: 18 pages Submitted from: a.zsak(a)dpmms.cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1409.3480 or http://arXiv.org/abs/1409.3480

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