Banach June 2012

banach@mathdept.okstate.edu

2 participants
26 discussions

Abstract of a paper by Pawel Kolwicz, Karol Lesnik, and Lech Maligranda
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "Pointwise multipliers of Calder\'on-Lozanovskii spaces" by Pawel Kolwicz, Karol Lesnik, and Lech Maligranda. Abstract: Several results concerning multipliers of symmetric Banach function spaces are presented firstly. Then the results on multipliers of Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on a Banach ideal space E and three Young functions \varphi_1, \varphi_2 and \varphi, generating the corresponding Calder\'on-Lozanovskii spaces E_{\varphi_1}, E_{\varphi_2}, E_{\varphi} so that the space of multipliers M(E_{\varphi_1}, E_{\varphi}) of all measurable x such that x,y \in E_{\varphi} for any y \in E_{\varphi_1} can be identified with E_{\varphi_2}. Sufficient conditions generalize earlier results by Ando, O'Neil, Zabreiko-Rutickii, Maligranda-Persson and Maligranda-Nakai. There are also necessary conditions on functions for the embedding M(E_{\varphi_1}, E_{\varphi}) \subset E_{\varphi_2} to be true, which already in the case when E = L^1, that is, for Orlicz spaces M(L^{\varphi_1}, L^{\varphi}) \subset L^{\varphi_2} give a solution of a problem raised in the book [Ma89]. Some properties of a generalized complementary operation on Young functions, defined by Ando, are investigated in order to show how to construct the function \varphi_2 such that M(E_{\varphi_1}, E_{\varphi}) = E_{\varphi_2}. There are also several examples of independent interest. Archive classification: math.FA Mathematics Subject Classification: Functional Analysis (math.FA) Remarks: 41 pages Submitted from: lech.maligranda(a)ltu.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.1860 or http://arXiv.org/abs/1206.1860

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Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "A hereditarily indecomposable Banach space with rich spreading model structure" by Spiros A. Argyros and Pavlos Motakis. Abstract: We present a reflexive Banach space $\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily Indecomposable and satisfies the following properties. In every subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists a weakly null normalized sequence $\{y_n\}_n$, such that every subsymmetric sequence $\{z_n\}_n$ is isomorphically generated as a spreading model of a subsequence of $\{y_n\}_n$. Also, in every block subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists a seminormalized block sequence $\{z_n\}$ and $T:\mathfrak{X}_{_{^\text{usm}}}\rightarrow\mathfrak{X}_{_{^\text{usm}}}$ an isomorphism such that for every $n\in\mathbb{N}$ $T(z_{2n-1}) = z_{2n}$. Thus the space is an example of an HI space which is not tight by range in a strong sense. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45 Remarks: 36 pages, no figures Submitted from: pmotakis(a)central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.1279 or http://arXiv.org/abs/1206.1279

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Abstract of a paper by Sergey V. Astashkin, Lech Maligranda and Konstantin E. Tikhomirov
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "New examples of K-monotone weighted Banach couples" by Sergey V. Astashkin, Lech Maligranda and Konstantin E. Tikhomirov. Abstract: Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X, X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is t^{1/p} for some p \in [1, \infty], then X = L_p. At the same time a Banach couple (X, X(w)) may be K-monotone for some non-trivial w in the case when X is not ultrasymmetric. In each of the cases where X is a Lorentz, Marcinkiewicz or Orlicz space we have found conditions which guarantee that (X, X(w)) is K-monotone. Archive classification: math.FA Mathematics Subject Classification: Functional Analysis (math.FA) Remarks: 31 pages Submitted from: lech.maligranda(a)ltu.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.1244 or http://arXiv.org/abs/1206.1244

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Abstract of a paper by Pierre Youssef
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "Restricted Invertibility and the Banach-Mazur distance to the cube" by Pierre Youssef. Abstract: We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization theorem recovering the best current estimate. As a consequence, we also recover the best known estimate for the Banach-Mazur distance to the cube: the distance of every n-dimensional normed space from \ell_{\infty }^n is at most (2n)^(5/6). Finally, using tools from the work of Batson-Spielman-Srivastava, we give a new proof for a theorem of Kashin-Tzafriri on the norm of restricted matrices. Archive classification: math.FA Submitted from: pierre.youssef(a)univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.0654 or http://arXiv.org/abs/1206.0654

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Abstract of a paper by Spiros A. Argyros, Antonis Manoussakis, and Anna Pelczar-Barwacz
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "A type (4) space in (FR)-classification" by Spiros A. Argyros, Antonis Manoussakis, and Anna 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. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis. Archive classification: math.FA Mathematics Subject Classification: 46B03 Remarks: 14 pages Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.0651 or http://arXiv.org/abs/1206.0651

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Abstract of a paper by Franck Barthe, Karoly J. Boroczky, and Matthieu Fradelizi
by alspach＠math.okstate.edu 22 Jun '12

22 Jun '12

This is an announcement for the paper "Stability of the functional forms of the Blaschke-Santalo inequality" by Franck Barthe, Karoly J. Boroczky, and Matthieu Fradelizi. Abstract: Stability versions of the functional forms of the Blaschke-Santalo inequality due to Ball, Artstein-Klartag-Milman, Fradelizi-Meyer and Lehec are proved. Archive classification: math.MG math.FA Submitted from: carlos(a)renyi.hu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1206.0369 or http://arXiv.org/abs/1206.0369

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SUMIRFAS announcement
by Bill Johnson 21 Jun '12

21 Jun '12

1st ANNOUNCEMENT OF SUMIRFAS 2012 The Informal Regional Functional Analysis Seminar August 3-5 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, whose NEW URL is http://www.math.tamu.edu/~kerr/workshop/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 169. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html. Coffee and refreshments will be available in Blocker 148. Speakers at SUMIRFAS 2012 include Pete Casazza Ed Effros Su Gao Ali Kavruk Masoud Khalkhali Izabella Laba Michael Lacey Paul Mueller Darrin Speegle Russ Thompson July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps Between Operator Algebras", organized by Chris Heil, Emily J. King (chair), Keri Kornelson, and Darrin Speegle. A researcher working in frame theory will naturally be led to consider matrices (the Gram matrix, the analysis operator and the synthesis operator), and many problems in frame theory have a re-casting in operator theory. The most celebrated example of this is the Kadison-Singer problem. By now, there are many mathematicians familiar with the basics of the two areas, and there is a fruitful collaboration. Less obvious is the relationship between frame theory and maps between operator algebras. Very recent work in this area by Han, Larson, Lu, and Lu indicate that this may be a relationship that is ripe for exploiting. The goal of this concentration week is to bring together researchers in these two fields so that they may learn from one another and build networks of potential collaborators. There will be introductory series of talks on "Frame theory" by Ole Christensen, on "Maps on Operator Algebras" by Vern Paulsen, and on "Bridging the Gap Between Frame Theory and Maps on Operator Algebras" by Deguang Han. This concentration week will also lead into a separate conference on the following weekend celebrating the 70th birthday of David Larson. The home page for this Workshop is at http://page.math.tu-berlin.de/~king/cw.html August 6-10 there will be a Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory", organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and Alexei Poltoratski. This CW is designed to bring together two groups of experts: those specializing in complex and harmonic analysis and those working in spectral theory of differential operators and mathematical physics. The main goals of the CW are to study new relationships and to widen further participation in this area in the United States. Introductory series of lectures by Stephen Gustafson, Svetlana Jitomirskaya, Helge Krueger, and Brett Wick are planned to acquaint non-experts with these topics with the reasonable expectation that some the participants in the larger Workshop will will be attracted to this program and inject new ideas into the area. The home page for this Workshop is at http://www.math.tamu.edu/~comech/events/hast-2012/ 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 "Frame Theory and Maps Between Operator Algebras" contact Emily King <eking(a)math.umd.edu> For information about the Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory" contact Constanze Liaw <conni(a)math.tamu.edu>

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Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "On the Gaussian behavior of marginals and the mean width of random polytopes" by David Alonso-Gutierrez and Joscha Prochno. Abstract: We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\leq N\leq e^{\sqrt n}$) uniformly distributed in an isotropic convex body in $\R^n$ is of the order $\sqrt{\log N} L_K$. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way. Archive classification: math.FA math.PR Mathematics Subject Classification: 52A22, 52A23, 05D40, 46B09 Submitted from: prochno(a)math.uni-kiel.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1205.6174 or http://arXiv.org/abs/1205.6174

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Abstract of a paper by Assaf Naor
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "An introduction to the Ribe program" by Assaf Naor. Abstract: This article accompanies the 10th Takagi Lectures, delivered by the author at RIMS, Kyoto, on May 26 2012. It contains an exposition of results, applications, and challenges of the Ribe program. Archive classification: math.FA math.MG Remarks: To appear in Japanese Journal of Mathematics Submitted from: naor(a)cims.nyu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1205.5993 or http://arXiv.org/abs/1205.5993

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Abstract of a paper by Ioannis Gasparis
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "A new isomorphic \ell_1 predual not isomorphic to a complemented subspace of a C(K) space" by Ioannis Gasparis. Abstract: An isomorphic $\ell_1$-predual space $X$ is constructed such that neither $X$ is isomorphic to a subspace of $c_0$, nor $C(\omega^\omega)$ is isomorphic to a subspace of $X$. It follows that $X$ is not isomorphic to a complemented subspace of a $C(K)$ space. Archive classification: math.FA Mathematics Subject Classification: 46B03 Remarks: 12 pages Submitted from: ioagaspa(a)math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/mod/1205.4317 or http://arXiv.org/abs/mod/1205.4317

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Banach June 2012