Banach

banach@mathdept.okstate.edu

2549 discussions

Workshop at A&M
by Bill Johnson 11 Apr '13

11 Apr '13

Workshop in Analysis and Probability Department of Mathematics Texas A&M University Summer 2013 The Summer 2013 Workshop in Analysis and Probability at Texas A&M University will be in session from July 15 until August 16, 2013. For information about the Workshop, consult the Workshop Home Page, whose URL is http://www.math.tamu.edu/~kerr/workshop/ The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held August 2-4. SUMIRFAS will be dedicated to the memory of Ted Odell, who was one of the organizers of the UTAMIRFAS, the predecessor of SUMIRFAS. Ted served on the advisory board of the Workshop since its beginning. Plenary speakers at SUMIRFAS include Stephen Dilworth, Steve Jackson, Masoud Khalkhali, Thomas Schlumprecht, Nicole Tomczak-Jaegermann, and Wilhelm Winter. August 5-9 there will be a Concentration Week on "Dynamics, Geometry, and Operator Algebras", organized by David Kerr and Guoliang Yu. This Concentration Week aims to promote connections between nuclearity, nuclear dimension, group C*-algebras and crossed products, topological and measurable dynamics, algebraic dynamics, entropy, dimensional ideas from coarse geometry, and K-theory with applications to topology. The program will feature lecture series by David Kerr, Stuart White, and Rufus Willett. The URL for this Concentration Week is http://www.math.tamu.edu/~kerr/concweek13/ Immediately preceding SUMIRFAS, on August 1, there will be a celebration of "The Mathematical Legacy of Ted Odell", organized by Thomas Schlumprecht. The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week on "Dynamics, Geometry, and Operator Algebras" contact David Kerr <kerr(a)math.tamu.edu>. For information about the day devoted to "The Mathematical Legacy of Ted Odell" contact Thomas Schlumprecht <schlump(a)math.tamu.edu>

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Abstract of a paper by Gideon Schechtman
by alspach＠math.okstate.edu 26 Mar '13

26 Mar '13

This is an announcement for the paper "Matrix subspaces of $L_1$" by Gideon Schechtman. Abstract: If $E=\{e_i\}$ and $F=\{f_i\}$ are two 1-unconditional basic sequences in $L_1$ with $E$ $r$-concave and $F$ $p$-convex, for some $1\le r<p\le 2$, then the space of matrices $\{a_{i,j}\}$ with norm $\|\{a_{i,j}\}\|_{E(F)}=\big\|\sum_k \|\sum_l a_{k,l}f_l\|e_k\big\|$ embeds into $L_1$. This generalizes a recent result of Prochno and Sch\"utt. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B45, 46B15 Submitted from: gideon(a)weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.4590 or http://arXiv.org/abs/1303.4590

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Abstract of a paper by A. Manoussakis and A. Pelczar-Barwacz
by alspach＠math.okstate.edu 26 Mar '13

26 Mar '13

This is an announcement for the paper "Types of tightness in spaces with unconditional basis" by A. Manoussakis and A. Pelczar-Barwacz. Abstract: We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces, but contrary to the recently constructed space of type (4) also tight with constants, thus essentially extending the list of known examples in Gowers classification program. The space is defined on the base on a boundedly modified mixed Tsirelson space with use of a special coding function. Archive classification: math.FA Mathematics Subject Classification: 46B03 Submitted from: amanousakis(a)isc.tuc.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.2370 or http://arXiv.org/abs/1303.2370

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Abstract of a paper by Robert Deville and Oscar Madiedo
by alspach＠math.okstate.edu 26 Mar '13

26 Mar '13

This is an announcement for the paper "A characterization of the Radon-Nikodym property" by Robert Deville and Oscar Madiedo. Abstract: It is well known that every bounded below and non increasing sequence in the real line converges. We give a version of this result valid in Banach spaces with the Radon-Nikodym property, thus extending a former result of A. Proch\'azka. Archive classification: math.FA Mathematics Subject Classification: 91A05, 46B20, 46B22 Remarks: 10 pages, 2 figures Submitted from: oscar.reynaldo(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.1721 or http://arXiv.org/abs/1303.1721

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Abstract of a paper by Tomasz Kania, Piotr Koszmider and Niels Jakob Laustsen
by alspach＠math.okstate.edu 26 Mar '13

26 Mar '13

This is an announcement for the paper "A weak*-topological dichotomy with applications in operator theory" by Tomasz Kania, Piotr Koszmider and Niels Jakob Laustsen. Abstract: Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\omega_1]$. Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\omega_1)$ can either be embedded in a Hilbert-generated Banach space, or it is isomorphic to the direct sum of $C_0[0,\omega_1)$ and a subspace of a Hilbert-generated Banach space. Moreover, we obtain a list of eight equivalent conditions describing the Loy--Willis ideal, which is the unique maximal ideal of the Banach algebra of bounded, linear operators on $C_0[0,\omega_1)$. As a consequence, we find that this ideal has a bounded left approximate identity, thus solving a problem left open by Loy and Willis, and we give new proofs, in some cases of stronger versions, of several known results about the Banach space $C_0[0,\omega_1)$ and the operators acting on it. Archive classification: math.FA math.GN Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1303.0020 or http://arXiv.org/abs/1303.0020

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Abstract of a paper by Piotr W. Nowak
by alspach＠math.okstate.edu 26 Mar '13

26 Mar '13

This is an announcement for the paper "Group actions on Banach spaces" by Piotr W. Nowak. Abstract: Recently there has been growing interest in extending Kazhdan's property (T) to other Banach spaces, but even for such familiar classes as the Lebesgue spaces $L_p$, or even spaces isomorphic to the Hilbert space, this program proved to be challenging. Our goal in this survey is to give a fairly complete account of the recent developments and their applications. We purposely focus only on the case of Banach spaces which are not Hilbert spaces, discussing the latter case mainly as motivation. Wa also discuss metrically proper actions on Banach spaces, their interplay with fixed point properties and geometric applications. Archive classification: math.GR math.DS math.FA math.OA Submitted from: pnowak(a)mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.6609 or http://arXiv.org/abs/1302.6609

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Nassif Ghoussoub Blog: Honoring Friends
by Dale Alspach 25 Mar '13

25 Mar '13

http://nghoussoub.com/2013/03/24/bill-joram-olek-ted-and-bob/

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Positivity VII
by Dale Alspach 28 Feb '13

28 Feb '13

The seventh Positivity conference will be held from July 22-26, 2013, at the science campus of Leiden University, The Netherlands, jointly organized by Leiden University and Delft University of Technology. As with earlier issues, the conference is dedicated to ordered structures and their applications in a broad sense, including topics such as ordered Banach spaces and their operators, ordered Banach algebras, ordering in operator algebras, etc. Invited speakers, all confirmed: Francesco Altomare (Bari, Italy) Wolfgang Arendt (Ulm, Germany) Karim Boulabiar (Tunis, Tunisia) Qingying Bu (University, Mississippi, USA) Guillermo Curbera (Sevilla, Spain) Julio Flores (Madrid, Spain) Yehoram Gordon (Haifa, Israel) Rien Kaashoek (Amsterdam, The Netherlands) Coenraad Labuschagne (Johannesburg, South Africa) Boris Mordukhovich (Detroit, Michigan, USA) Jan van Neerven (Delft, The Netherlands) Ioannis Polyrakis (Athens, Greece) Abdelaziz Rhandi (Salerno, Italy) Evgeny Semenov (Voronezh, Russia) Fedor Sukochev (Sydney, Australia) Jun Tomiyama (Tokyo, Japan) All participants will be given the opportunity for a 30 minute contributed talk. More details, and a list of the currently 130 pre-registered participants, can be found at http://websites.math.leidenuniv.nl/positivity2013/ For further information, or for inclusion in the mailing list of the conference, please contact the organizers at <positivity2013(a)gmail.com>. ********************************************************* ------------------------------------------------------------------------ Marcel de Jeu Leiden University Tel. (office) +31 (0)71 527 7118 Mathematical Institute Tel. (general) +31 (0)71 527 7111 P.O. Box 9512 Fax +31 (0)71 527 7101 2300 RA Leiden email mdejeu(a)math.leidenuniv.nl The Netherlands URL http://www.math.leidenuniv.nl/~mdejeu/ ------------------------------------------------------------------------

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Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "On quantitative Schur and Dunford-Pettis properties" by Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We show that the dual to any subspace of $c_0(\Gamma)$ has the strongest possible quantitative version of the Schur property. Further, we establish relationship between the quantitative Schur property and quantitative versions of the Dunford-Pettis property. Finally, we apply these results to show, in particular, that any subspace of the space of compact operators on $\ell_p$ ($1<p<\infty$) with Dunford-Pettis property satisfies automatically both its quantitative versions. Archive classification: math.FA Mathematics Subject Classification: 46B25 Remarks: 10 pages Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.6369 or http://arXiv.org/abs/1302.6369

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Abstract of a paper by Tomasz Kania and Tomasz Kochanek
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Steinhaus' lattice-point problem for Banach spaces" by Tomasz Kania and Tomasz Kochanek. Abstract: Given a positive integer $n$, one may find a circle surrounding exactly $n$ points of the integer lattice. This classical geometric fact due to Steinhaus has been recently extended to Hilbert spaces by Zwole\'{n}ski, who replaced the integer lattice by any infinite set which intersects every ball in at most finitely many points. We investigate the norms satisfying this property, which we call (S), and show that all strictly convex norms have (S). Nonetheless, we construct a norm in dimension three which has (S) but fails to be strictly convex. Furthermore, the problem of finding an equivalent norm enjoying (S) is studied. With the aid of measurable cardinals, we prove that there exists a Banach space having (S) but with no strictly convex renorming. Archive classification: math.FA Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.6443 or http://arXiv.org/abs/1302.6443

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