February 2013 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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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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Abstract of a paper by Matthieu Fradelizi and Arnaud Marsiglietti
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "On the analogue of the concavity of entropy power in the Brunn-Minkowski theory" by Matthieu Fradelizi and Arnaud Marsiglietti. Abstract: Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\it On the similarity of the entropy power inequality and the Brunn-Minkowski inequality} (IEEE Trans. Inform. Theory 30 (1984), no. 6, 837-839) the $\frac{1}{n}$-concavity of the outer parallel volume of measurable sets as an analogue of the concavity of entropy power. We investigate this conjecture and study its relationship with geometric inequalities. Archive classification: math.FA cs.IT math.IT math.MG Mathematics Subject Classification: 52A40, 94A17 Submitted from: matthieu.fradelizi(a)univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.6093 or http://arXiv.org/abs/1302.6093

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Abstract of a paper by Oleg Reinov and Asfand Fahad
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "On dentability in locally convex vector spaces" by Oleg Reinov and Asfand Fahad. Abstract: For a locally convex vector space (l.c.v.s.) $E$ and an absolutely convex neighborhood $V$ of zero, a bounded subset $A$ of $E$ is said to be $V$-dentable (respectively, $V$-f-dentable) if for any $\epsilon>0$ there exists an $x\in A$ so that $$x\notin \overline{co} (A\setminus (x+\epsilon V)) $$ (respectively, so that $$ x\notin {co} (A\setminus (x+\epsilon V)) ). $$ Here, "$\overline{co}$" denotes the closure in $E$ of the convex hull of a set. We present a theorem which says that for a wide class of bounded subsets $B$ of locally convex vector spaces the following is true: $(V)$ every subset of $B$ is $V$-dentable if and only if every subset of $B$ is $V$-f-dentable. The proof is purely geometrical and independent of any related facts. As a consequence (in the particular case where $B$ is complete convex bounded metrizable subset of a l.c.v.s.), we obtain a positive solution to a 1978-hypothesis of Elias Saab (see p. 290 in "On the Radon-Nikodym property in a class of locally convex spaces", Pacific J. Math. 75, No. 1, 1978, 281-291). Archive classification: math.FA Remarks: 5 pages, AMSTeX Submitted from: orein51(a)mail.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.6019 or http://arXiv.org/abs/1302.6019

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Abstract of a paper by Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "On metric characterizations of the Radon-Nikodym and related properties of Banach spaces" by Mikhail I. Ostrovskii. Abstract: We find a class of metric structures which do not admit bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym property. Our proof relies on Chatterji's (1968) martingale characterization of the RNP and does not use the Cheeger's (1999) metric differentiation theory. The class includes the infinite diamond and both Laakso (2000) spaces. We also show that for each of these structures there is a non-RNP Banach space which does not admit its bilipschitz embedding. We prove that a dual Banach space does not have the RNP if and only if it admits a bilipschitz embedding of the infinite diamond. The paper also contains related characterizations of reflexivity and the infinite tree property. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 46B22, Secondary: 05C12, 30L05, 46B10, 46B85, 54E35 Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.5968 or http://arXiv.org/abs/1302.5968

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Abstract of a paper by Jaegil Kim and Artem Zvavitch
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Stability of the reverse Blaschke-Santalo inequality for unconditional convex bodies" by Jaegil Kim and Artem Zvavitch. Abstract: Mahler's conjecture asks whether the cube is a minimizer for the volume product of a body and its polar in the class of symmetric convex bodies in R^n. The corresponding inequality to the conjecture is sometimes called the the reverse Blaschke-Santalo inequality. The conjecture is known in dimension two and in several special cases. In the class of unconditional convex bodies, Saint Raymond confirmed the conjecture, and Meyer and Reisner, independently, characterized the equality case. In this paper we present a stability version of these results and also show that any symmetric convex body, which is sufficiently close to an unconditional body, satisfies the the reverse Blaschke-Santalo inequality. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15, 52B10 Submitted from: jkim(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.5719 or http://arXiv.org/abs/1302.5719

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Abstract of a paper by Claudia Correa and Daniel V. Tausk
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Extension property and complementation of isometric copies of continuous functions spaces" by Claudia Correa and Daniel V. Tausk. Abstract: In this article we prove that every isometric copy of C(L) in C(K) is complemented if L is compact Hausdorff of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an extension operator. The space C(L) can be replaced by its subspace C(L|F) consisting of functions that vanish on a closed subset F of L. In particular, we obtain that every isometric copy of c_0(I) in C(K) is complemented, if K has the extension property. Finally, we study the class of spaces having the extension property, establishing some closure results for this class and relating it to other classes of compact spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46E15, 54G12 Remarks: 9 pages Submitted from: tausk(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.4661 or http://arXiv.org/abs/1302.4661

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Abstract of a paper by Grzegorz Plebanek
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "On positive embeddings of C(K) spaces" by Grzegorz Plebanek. Abstract: We investigate isomorphic embeddings $T: C(K)\to C(L)$ between Banach spaces of continuous functions. We show that if such an embedding $T$ is a positive operator then $K$ is an image of $L$ under a upper semicontinuous set-function having finite values. Moreover we show that $K$ has a $\pi$-base of sets which closures a continuous images of compact subspaces of $L$. Our results imply in particular that if $C(K)$ can be positively embedded into $C(L)$ then some topological properties of $L$, such as countable tightness of Frechetness, pass to the space $K$. We show that some arbitrary isomorphic embeddings $C(K)\to C(L)$ can be, in a sense, reduced to positive embeddings. Archive classification: math.FA Submitted from: grzes(a)math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.4360 or http://arXiv.org/abs/1302.4360

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