Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "Operators whose dual has non-separable range" by Pandelis Dodos. Abstract: Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$. Archive classification: math.FA Remarks: 20 pages, no figures Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2666 or http://arXiv.org/abs/1006.2666

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Abstract of a paper by Kevin Benaland and Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "On strictly singular operators between separable Banach spaces" by Kevin Beanland and Pandelis Dodos. Abstract: Let $X$ and $Y$ be separable Banach spaces and denote by $\sss\sss(X,Y)$ the subset of $\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\sss\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\rs$ on $\sss\sss(X,Y)$. We show that $\rs$ is a co-analytic rank and that dominates the rank $\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\leq p<+\infty$ we construct a Banach space $Y_p$ with an unconditional basis such that $\sss\sss(\ell_p, Y_p)$ is a co-analytic non-Borel subset of $\llll(\ell_p,Y_p)$ yet every strictly singular operator $T:\ell_p\to Y_p$ satisfies $\varrho(T)\leq 2$. This answers a question of Argyros. Archive classification: math.FA Remarks: 20 pages, no figures; Mathematika, to appear Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2672 or http://arXiv.org/abs/1006.2672

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "Quotients of Banach spaces and surjectively universal spaces" by Pandelis Dodos. Abstract: We characterize those classes $\mathcal{C}$ of separable Banach spaces for which there exists a separable Banach space $Y$ not containing $\ell_1$ and such that every space in the class $\mathcal{C}$ is a quotient of $Y$. Archive classification: math.FA Citation: Studia Mathematica 197 (2010), 171-194 Remarks: 23 pages, no figures Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2665 or http://arXiv.org/abs/1006.2665

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New Journal - Annals of Functional Analysis
by Dale Alspach 06 Jul '10

06 Jul '10

Dear colleague, It is my pleasure to invite you to submit a research paper of high standard or critical survey paper for possible publication in the electronic journal. "Annals of Functional Analysis (AFA)" http://www.emis.de/journals/AFA/ It would be appreciated if you promote the journal among your fellow-workers and colleagues. Best wishes M. S. Moslehian Editor-in-chief of AFA ********************************************** Mohammad Sal Moslehian Ph.D., Professor of Mathematics Address: Dept. of Pure Math., P.O. Box 1159 Ferdowsi University of Mashhad Mashhad 91775, Iran Mobile: (+98)(9151140894) Tel-Fax: (+98)(511)(8828606) E-mails: moslehian(a)ams.org moslehian(a)um.ac.ir Home: http://www.um.ac.ir/~moslehian/ **********************************************

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Abstract of a paper by Catalin Badea, Sophie Grivaux and Vladimir Muller
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "The rate of convergence in the method of alternating projections" by Catalin Badea, Sophie Grivaux and Vladimir Muller. Abstract: A generalization of the cosine of the Friedrichs angle between two subspaces to a parameter associated to several closed subspaces of a Hilbert space is given. This parameter is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick uniform convergence versus arbitrarily slow convergence) holds. Several meanings for ASC are proposed. Archive classification: math.FA math.NA Remarks: 23 pages, to appear in St. Petersburg Math J. (2010) Submitted from: catalin.badea(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2047 or http://arXiv.org/abs/1006.2047

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Abstract of a paper by Catalin Badea and Yuri I. Lyubich
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces" by Catalin Badea and Yuri I. Lyubich. Abstract: According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum. Archive classification: math.FA Remarks: 22 pages Submitted from: catalin.badea(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2052 or http://arXiv.org/abs/1006.2052

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Abstract of a paper by Jaegil Kim, Vladyslav Yaskin and Artem Zvavitch
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "The geometry of p-convex intersection bodies" by Jaegil Kim, Vladyslav Yaskin and Artem Zvavitch. Abstract: Busemann's theorem states that the intersection body of an origin-symmetric convex body is also convex. In this paper we provide a version of Busemann's theorem for p-convex bodies. We show that the intersection body of a p-convex body is q-convex for certain q. Furthermore, we discuss the sharpness of the previous result by constructing an appropriate example. This example is also used to show that IK, the intersection body of K, can be much farther away from the Euclidean ball than K. Finally, we extend these theorems to some general measure spaces with log-concave and $s$-concave measures Archive classification: math.FA Mathematics Subject Classification: 44A12, 52A15, 52A21 Submitted from: zvavitch(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.1546 or http://arXiv.org/abs/1006.1546

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Abstract of a paper by Geraldo Botelho, Erhan Caliskan and Daniel Pellegrino
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "On the representation of multi-ideals by tensor norms" by Geraldo Botelho, Erhan Caliskan and Daniel Pellegrino. Abstract: A tensor norm isomorphism. In this paper we study the representation of multi-ideals and of ideals of multilinear forms by smooth tensor norms Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.1540 or http://arXiv.org/abs/1006.1540

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Abstract of a paper by Konrad J. Swanepoel
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "Sets of unit vectors with small pairwise sums" by Konrad J. Swanepoel. Abstract: We study the sizes of delta-additive sets of unit vectors in a d-dimensional normed space: the sum of any two vectors has norm at most delta. One-additive sets originate in finding upper bounds of vertex degrees of Steiner Minimum Trees in finite dimensional smooth normed spaces (Z. F\"uredi, J. C. Lagarias, F. Morgan, 1991). We show that the maximum size of a delta-additive set over all normed spaces of dimension d grows exponentially in d for fixed delta>2/3, stays bounded for delta<2/3, and grows linearly at the threshold delta=2/3. Furthermore, the maximum size of a 2/3-additive set in d-dimensional normed space has the sharp upper bound of d, with the single exception of spaces isometric to three-dimensional l^1 space, where there exists a 2/3-additive set of four unit vectors. Archive classification: math.MG math.FA Mathematics Subject Classification: Primary 46B20. Secondary 52A21, 52B10 Citation: Quaestiones Mathematicae 23 (2000) 383-388 Remarks: 6 pages. Old paper of 10 years ago Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.1051 or http://arXiv.org/abs/1006.1051

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Abstract of a paper by F. Dadipour and M. S. Moslehian
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "A characterization of inner product spaces related to the p-angular distance" by F. Dadipour and M. S. Moslehian. Abstract: In this paper we present a new characterization of inner product spaces related to the p-angular distance. We also generalize some results due to Dunkl, Williams, Kirk, Smiley and Al-Rashed by using the notion of p-angular distance. Archive classification: math.FA Mathematics Subject Classification: Primary 46C15, Secondary 46B20, 46C05 Remarks: 9 Pages, to appear in J. Math. Anal. Appl. (JMAA) 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/1006.1022 or http://arXiv.org/abs/1006.1022

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