January 2010 - 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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Conference Announcement
by Dale Alspach 08 Jan '10

08 Jan '10

The 6th Conference on Function Spaces will be held at the SIUE campus near St. Louis between May 17 and May 22, 2010. More information may be found at: http://www.siue.edu/MATH/conference2010/ The organizer received a small grant to defray the attendance cost; according to the NSF rules priority will be given to young mathematicians (including graduate students) without other sources of support. Krzysztof Jarosz Department of Mathematics and Statistics Southern Illinois University Edwardsville Edwardsville, IL 62026-1653, USA tel.: (618) 650-2354 fax: (618) 650-3771 e-mail: kjarosz(a)siue.edu http://www.siue.edu/~kjarosz/

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Abstract of a paper by Vyacheslav V. Chistyakov and Yuliya V. Tretyachenko
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "Maps of several variables of finite total variation and Helly-type selection principles" by Vyacheslav V. Chistyakov and Yuliya V. Tretyachenko. Abstract: Given a map from a rectangle in the n-dimensional real Euclidean space into a metric semigroup, we introduce a concept of the total variation, which generalizes a similar concept due to T. H. Hildebrandt (1963) for real functions of two variables and A. S. Leonov (1998) for real functions of n variables, and study its properties. We show that the total variation has many classical properties of Jordan's variation such as the additivity, generalized triangle inequality and sequential lower semicontinuity. We prove two variants of a pointwise selection principle of Helly-type, one of which is as follows: a pointwise precompact sequence of metric semigroup valued maps on the rectangle, whose total variations are uniformly bounded, admits a pointwise convergent subsequence. Archive classification: math.FA Mathematics Subject Classification: 26B30 (Primary); 20M15; 28A20 (Secondary) Remarks: 47 pages, LaTeX, uses elsarticle.sty The source file(s), HSP_arX.tex: 126875 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0451 or http://arXiv.org/abs/1001.0451 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0451 or in gzipped form by using subject line get 1001.0451 to: math(a)arXiv.org.

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Abstract of a paper by Narinder S Claire
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "The spectral mapping theorem" by Narinder S Claire. Abstract: We prove the Spectral Mapping Theorem for the Helffer-Sj\"ostrand functional calculus for linear operators on Banach spaces with real spectra and consequently give a new proof for the Spectral Mapping Theorem for self-adjoint operators on Hilbert spaces. Archive classification: math.SP math.FA Mathematics Subject Classification: 47A60 Remarks: latex 12 pages The source file(s), integral.eps: 33099 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0232 or http://arXiv.org/abs/1001.0232 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0232 or in gzipped form by using subject line get 1001.0232 to: math(a)arXiv.org.

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Abstract of a paper by Jaegil Kim and Shlomo Reisner
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "Local minimality of the volume-product at the simplex" by Jaegil Kim and Shlomo Reisner. Abstract: It is proved that the simplex is a strict local minimum for the volume-product P(K)=min vol(K)vol(K^z), in the Banach-Mazur space of n-dimensional (classes of ) convex bodies. Here K^z is the polar body of K about the point z and the minimum is taken over all the points z in the interior of K. Linear local stability in the neighborhood of the simplex is proved as well. In the proof, methods that were recently introduced by Nazarov, Petrov, Ryabogin and Zvavitch are extended to the non-symmetric setting. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A40 The source file(s), KR-loc-min-simplex.tex: 34954 bytes, is(are) stored in gzipped form as 1001.0217.gz with size 12kb. The corresponding postcript file has gzipped size 84kb. Submitted from: reisner(a)math.haifa.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0217 or http://arXiv.org/abs/1001.0217 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0217 or in gzipped form by using subject line get 1001.0217 to: math(a)arXiv.org.

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Abstract of a paper by Piotr Indyk and Stanislaw Szarek
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "A simple construction of almost-Euclidean subspaces of $\ell_1^N$ via tensor products" by Piotr Indyk and Stanislaw Szarek. Abstract: It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding arbitrarily small distortions, or "almost Euclidean" subspaces. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B25, 52A21, 68P30 Remarks: 10 pages The source file(s), tensoring3e.tex: 37038 bytes, is(are) stored in gzipped form as 1001.0041.gz with size 13kb. The corresponding postcript file has gzipped size 99kb. Submitted from: szarek(a)cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.0041 or http://arXiv.org/abs/1001.0041 or by email in unzipped form by transmitting an empty message with subject line uget 1001.0041 or in gzipped form by using subject line get 1001.0041 to: math(a)arXiv.org.

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Abstract of a paper by F. Baudier, N. J. Kalton, and G. Lancien
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "A new metric invariant for Banach spaces" by F. Baudier, N. J. Kalton, and G. Lancien. Abstract: We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into $X$. We show that the converse is true when $X$ is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20; 46T99 Remarks: 22 pages The source file(s), new_invariant_BKL.tex: 63462 bytes, is(are) stored in gzipped form as 0912.5113.gz with size 19kb. The corresponding postcript file has gzipped size 132kb. Submitted from: florent.baudier(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.5113 or http://arXiv.org/abs/0912.5113 or by email in unzipped form by transmitting an empty message with subject line uget 0912.5113 or in gzipped form by using subject line get 0912.5113 to: math(a)arXiv.org.

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Abstract of a paper by Mohammed Yahdi
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "A coanalytic rank on super-ergodic operators" by Mohammed Yahdi. Abstract: Techniques from Descriptive Set Theory are applied in order to study the Topological Complexity of families of operators naturally connected to ergodic operators in infinite dimensional Banach Spaces. The families of ergodic, uniform-ergodic,Cesaro-bounded and power-bounded operators are shown to be Borel sets, while the family of super-ergodic operators is shown to be either coanalytic or Borel according to specific structures of the Space. Moreover, trees and coanalytic ranks are introduced to characterize super-ergodic operators as well as spaces where the above classes of operators do not coincide. Archive classification: math.GN math.FA Mathematics Subject Classification: 47A35; 54H05 Remarks: 9 pages The source file(s), YahdiCoanalyticRankOnSuperErgodicOperators.tex: 28531 bytes, is(are) stored in gzipped form as 0912.5389.gz with size 9kb. The corresponding postcript file has gzipped size 80kb. Submitted from: myahdi(a)ursinus.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.5389 or http://arXiv.org/abs/0912.5389 or by email in unzipped form by transmitting an empty message with subject line uget 0912.5389 or in gzipped form by using subject line get 0912.5389 to: math(a)arXiv.org.

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Abstract of a paper by Mark Kozdoba
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "On the smallest L_2 projection of a curve in R^n" by Mark Kozdoba. Abstract: For a curve T:[0,1] -> R^n, we consider the directions theta in R^n which T "misses" the most and quantify this, as a function of the L_2 norm of T's differential. Archive classification: math.FA The source file(s), curvL2arch.tex: 21640 bytes, is(are) stored in gzipped form as 0912.5323.gz with size 8kb. The corresponding postcript file has gzipped size 79kb. Submitted from: marikk(a)tx.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.5323 or http://arXiv.org/abs/0912.5323 or by email in unzipped form by transmitting an empty message with subject line uget 0912.5323 or in gzipped form by using subject line get 0912.5323 to: math(a)arXiv.org.

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Abstract of a paper by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza
by alspach＠fourier.math.okstate.edu 07 Jan '10

07 Jan '10

This is an announcement for the paper "Some new thin sets of integers in Harmonic Analysis" by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza. Abstract: We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in $\Lambda$ have uniformly convergent series, and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_\Lambda$ are equal for $q<+\infty$. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded functions with spectrum in $\Lambda$ is non separable. So these sets are very different from the thin sets of integers previously known. Archive classification: math.FA Mathematics Subject Classification: MSC: Primary: 42A36 ; 42A44 ; 42A55 ; 42A61 ; 43A46; Secondary: The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.4214 or http://arXiv.org/abs/0912.4214 or by email in unzipped form by transmitting an empty message with subject line uget 0912.4214 or in gzipped form by using subject line get 0912.4214 to: math(a)arXiv.org.

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