Banach February 2011

banach@mathdept.okstate.edu

2 participants
28 discussions

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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Abstract of a paper by Remi Gribonval and Morten Nielsen
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "The restricted isometry property meets nonlinear approximation with redundant frames" by Remi Gribonval and Morten Nielsen. Abstract: It is now well known that sparse or compressible vectors can be stably recovered from their low-dimensional projection, provided the projection matrix satisfies a Restricted Isometry Property (RIP). We establish new implications of the RIP with respect to nonlinear approximation in a Hilbert space with a redundant frame. The main ingredients of our approach are: a) Jackson and Bernstein inequalities, associated to the characterization of certain approximation spaces with interpolation spaces; b) a new proof that for overcomplete frames which satisfy a Bernstein inequality, these interpolation spaces are nothing but the collection of vectors admitting a representation in the dictionary with compressible coefficients; c) the proof that the RIP implies Bernstein inequalities. As a result, we obtain that in most overcomplete random Gaussian dictionaries with fixed aspect ratio, just as in any orthonormal basis, the error of best $m$-term approximation of a vector decays at a certain rate if, and only if, the vector admits a compressible expansion in the dictionary. Yet, for mildly overcomplete dictionaries with a one-dimensional kernel, we give examples where the Bernstein inequality holds, but the same inequality fails for even the smallest perturbation of the dictionary. Archive classification: math.FA Report Number: RR-7548 Remarks: This work has been submitted for possible publication. Copyright be transferred without notice, after which this version may no longer be accessible. Submitted from: remi.gribonval(a)inria.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.5324 or http://arXiv.org/abs/1102.5324

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Abstract of a paper by Greg Kuperberg
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Norms as a function of p are linearly independent in finite dimensions" by Greg Kuperberg. Abstract: We show that there are no non-trivial linear dependencies among p-norms of vectors in finite dimensions that hold for all p. The proof is by analytic continuation and a theorem of Ritt. Archive classification: math.FA Remarks: 1 page, 1 figure Submitted from: greg(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.5026 or http://arXiv.org/abs/1102.5026

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Abstract of a paper by Mikhail Ostrovskii
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "On metric characterizations of some classes of Banach spaces" by Mikhail Ostrovskii. Abstract: The paper contains the following results and observations: (1) There exists a sequence of unweighted graphs $\{G_n\}_n$ with maximum degree $3$ such that a Banach space $X$ has no nontrivial cotype iff $\{G_n\}_n$ admit uniformly bilipschitz embeddings into $X$; (2) The same for Banach spaces with no nontrivial type; (3) A sequence $\{G_n\}$ characterizing Banach spaces with no nontrivial cotype in the sense described above can be chosen to be a sequence of bounded degree expanders; (4) The infinite diamond does not admit a bilipschitz embedding into Banach spaces with the Radon-Nikod\'{y}m property; (5) A new proof of the Cheeger-Kleiner result: The Laakso space does not admit a bilipschitz embedding into Banach spaces with the Radon-Nikod\'{y}m property; (6) A new proof of the Johnson-Schechtman result: uniform bilipschitz embeddability of finite diamonds into a Banach space implies its nonsuperreflexivity. Archive classification: math.FA math.MG Mathematics Subject Classification: 46B85, Secondary: 05C12, 46B07, 46B22, 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/1102.5082 or http://arXiv.org/abs/1102.5082

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Frank Bonsall
by Jonathan Partington 28 Feb '11

28 Feb '11

We regret to say that Professor Frank Bonsall FRS, well known for his work in functional analysis, in particular, Banach algebras, numerical ranges and operator theory, died in Harrogate, Yorkshire on Tuesday February 22nd. He was 90 years old. Jonathan Partington, University of Leeds, UK

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Abstract of a paper by Jin Xi Chen, Zi Li Chen and Guo Xing Ji
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Order continuous extensions of positive compact operators on Banach lattices" by Jin Xi Chen, Zi Li Chen and Guo Xing Ji. Abstract: Let $E$ and $F$ be Banach lattices. Let $G$ be a vector sublattice of $E$ and $T: G\rightarrow F$ be an order continuous positive compact (resp. weakly compact) operators. We show that if $G$ is an ideal or an order dense sublattice of $E$, then $T$ has a norm preserving compact (resp. weakly compact) positive extension to $E$ which is likewise order continuous on $E$. In particular, we prove that every compact positive orthomorphism on an order dense sublattice of $E$ extends uniquely to a compact positive orthomorphism on $E$. Archive classification: math.FA Remarks: 7 pages Submitted from: jinxichen(a)home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.4912 or http://arXiv.org/abs/1102.4912

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Abstract of a paper by A. Thiago Lopes Bernardino
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "On cotype and inclusions for absolutely summing multilinear operators" by A. Thiago Lopes Bernardino. Abstract: In this note we improve previous results on inclusion theorems for absolutely summing multilinear operators. Archive classification: math.FA Remarks: 3 pages Submitted from: thiagodcea(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.4542 or http://arXiv.org/abs/1102.4542

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Abstract of a paper by Stefano Rossi
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "On a class of $C^*$ preduals of $l_1$" by Stefano Rossi. Abstract: Some nice preduals of $l_1$ are presented Archive classification: math.FA Remarks: 5 pages Submitted from: s-rossi(a)mat.uniroma1.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.4325 or http://arXiv.org/abs/1102.4325

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Abstract of a paper by Veronica Dimant and Silvia Lassalle
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "$M$-structures in vector-valued polynomial spaces" by Veronica Dimant and Silvia Lassalle. Abstract: This paper is concerned with the study of $M$-structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\mathcal P_w(^n E, F)$, is an $M$-ideal in the space of continuous $n$-homogeneous polynomials $\mathcal P(^n E, F)$. We show that there is some hope for this to happen only for a finite range of values of $n$. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when $E=\ell_p$ and $F=\ell_q$ or $F$ is a Lorentz sequence space $d(w,q)$. We extend to our setting the notion of property $(M)$ introduced by Kalton which allows us to lift $M$-structures from the linear to the vector-valued polynomial context. Also, when $\mathcal P_w(^n E, F)$ is an $M$-ideal in $\mathcal P(^n E, F)$ we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets. Archive classification: math.FA Mathematics Subject Classification: 47H60, 46B04, 47L22, 46B20 Submitted from: vero(a)udesa.edu.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.3850 or http://arXiv.org/abs/1102.3850

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Abstract of a paper by Franck Barthe, Chiara Bianchini, and Andrea Colesanti
by alspach＠math.okstate.edu 28 Feb '11

28 Feb '11

This is an announcement for the paper "Isoperimetry and stability of hyperplanes for product probability measures" by Franck Barthe, Chiara Bianchini, and Andrea Colesanti. Abstract: We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure. Archive classification: math.FA math.PR Submitted from: chiara.bianchini(a)iecn.u-nancy.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1102.3621 or http://arXiv.org/abs/1102.3621

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Banach February 2011