August 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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Abstract of a paper by Leandro Candido
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "On embeddings of $C_0(K)$ spaces into $C_0(J,X)$ spaces" by Leandro Candido. Abstract: Let $C_0(K, X)$ denote the space of all continuous $X$-valued functions defined on the locally compact Hausdorff space $K$ which vanish at infinity, provided with the supremum norm. If $X$ is the scalar field, we denote $C_0(K, X)$ by simply $C_0(K)$. If $K$ is compact these spaces will be denoted by $C(K,X)$ and $C(K)$ respectively. In this paper we study whether some aspects of the space $K$ are determined by $J$ and the geometry of the Banach space $X$, if there is a linear embeddind of $C_0(K)$ into $C_0(J,X)$. Archive classification: math.FA Mathematics Subject Classification: Primary 46E40, Secondary 46B25 Submitted from: lc(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6555 or http://arXiv.org/abs/1308.6555

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Abstract of a paper by Michael Dymond
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Avoiding sigma-porous sets in Hilbert spaces" by Michael Dymond. Abstract: We give a constructive proof that any $\sigma$-porous subset of a Hilbert space has Lebesgue measure zero on typical $C^{1}$ curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-$p$ porous sets may meet many $C^{1}$ curves in positive measure. Archive classification: math.FA Submitted from: dymondm(a)maths.bham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6420 or http://arXiv.org/abs/1308.6420

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Abstract of a paper by Hui Zhang and Lizhi Cheng
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "New bounds for circulant Johnson-Lindenstrauss embeddings" by Hui Zhang and Lizhi Cheng. Abstract: This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound $k=O(\epsilon^{-2}\log^{(1+\delta)} (n))$ for Gaussian circulant JL embeddings. Moreover, by using the Laplace transform technique (also called Bernstein's trick), we extend the result to subgaussian case. The bounds in this paper offer a small improvement over the current best bounds for Gaussian circulant JL embeddings for certain parameter regimes and are derived using more direct methods. Archive classification: cs.IT math.FA math.IT Remarks: 11 pages; accepted by Communications in Mathematical Sciences Submitted from: h.zhang1984(a)163.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6339 or http://arXiv.org/abs/1308.6339

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Abstract of a paper by Fernando Albiac and Jose L Ansorena
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Optimal average approximations for functions mapping in quasi-Banach spaces" by Fernando Albiac and Jose L Ansorena. Abstract: In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1, and the question arose whether such a significant result might hold in some non-Banach spaces. In this article we completely settle the problem by proving that the fundamental theorem of calculus breaks down in the context of any non-locally convex quasi-Banach space. Our approach introduces the tool of Riemann-integral averages of continuous functions, and uses it to bring out to light the differences in behavior of their approximates in the lack of local convexity. As a by-product of our work we solve a problem raised in [F. Albiac and J.L. Ansorena, Lipschitz maps and primitives for continuous functions in quasi-Banach space, Nonlinear Anal. 75 (2012), no. 16, 6108-6119] on the different types of spaces of differentiable functions with values on a quasi-Banach space. Archive classification: math.FA Mathematics Subject Classification: 46A16, 46G05 Remarks: 14 pages Submitted from: joseluis.ansorena(a)unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6127 or http://arXiv.org/abs/1308.6127

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Abstract of a paper by Emanuel Milman and Liran Rotem
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Complemented Brunn--Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures" by Emanuel Milman and Liran Rotem. Abstract: Elementary proofs of sharp isoperimetric inequalities on a normed space $(\Real^n,\norm{\cdot})$ equipped with a measure $\mu = w(x) dx$ so that $w^p$ is homogeneous are provided, along with a characterization of the corresponding equality cases. When $p \in (0,\infty]$ and in addition $w^p$ is assumed concave, the result is an immediate corollary of the Borell--Brascamp--Lieb extension of the classical Brunn--Minkowski inequality, providing an elementary proof of a recent result of Cabr\'e--Ros Oton--Serra. When $p \in (-1/n,0)$, the relevant property turns out to be a novel ``complemented Brunn--Minkowski" inequality, which we show is always satisfied by $\mu$ when $w^p$ is homogeneous. This gives rise to a new class of measures, which are ``complemented" analogues of the class of convex measures introduced by Borell, but which have vastly different properties. The resulting isoperimetric inequality and characterization of isoperimetric minimizers extends beyond the recent results of Ca\~{n}ete--Rosales and Howe. The isoperimetric and Brunn-Minkowski type inequalities extend to the non-homogeneous setting, under a certain log-convexity assumption on the density. Finally, we obtain functional, Sobolev and Nash-type versions of the studied inequalities. Archive classification: math.FA math.MG Remarks: 37 pages Submitted from: emanuel.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.5695 or http://arXiv.org/abs/1308.5695

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Abstract of a paper by Ryan Causey
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces" by Ryan Causey. Abstract: For each ordinal $\alpha< \omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices $Sz(X), Sz(X^*)$ do not exceed $\omega^\alpha$. Archive classification: math.FA Submitted from: rcausey(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.5416 or http://arXiv.org/abs/1308.5416

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Abstract of a paper by Volker W. Thurey
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "The complex angle in normed spaces" by Volker W. Thurey. Abstract: We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This `angle' has some simple properties, which are known from the usual angle in real inner product spaces. But to do ordinary Euclidean geometry real angles are necessary. We show that even in a complex normed space there are many pure real valued `angles'. The situation improves yet in inner product spaces. There we can use the known theory of orthogonal systems to find many pairs of vectors with real angles, and to do geometry which is based on the Greeks 2000 years ago. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46C05, 30E99 Remarks: 21 pages Submitted from: volker(a)thuerey.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.5412 or http://arXiv.org/abs/1308.5412

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Abstract of a paper by Miguel Lacruz and Luis Rodriguez-Piazza
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Localizing algebras and invariant subspaces" by Miguel Lacruz and Luis Rodriguez-Piazza. Abstract: It is shown that the algebra $L^\infty(\mu)$ of all bounded measurable functions with respect to a finite measure $\mu$ is localizing on the Hilbert space $L^2(\mu)$ if and only if the measure $\mu$ has an atom. Next, it is shown that the algebra $H^\infty({\mathbb D})$ of all bounded analytic multipliers on the unit disc fails to be localizing, both on the Bergman space $A^2({\mathbb D})$ and on the Hardy space $H^2({\mathbb D}).$ Then, several conditions are provided for the algebra generated by a diagonal operator on a Hilbert space to be localizing. Finally, a theorem is provided about the existence of hyperinvariant subspaces for operators with a localizing subspace of extended eigenoperators. This theorem extends and unifies some previously known results of Scott Brown and Kim, Moore and Pearcy, and Lomonosov, Radjavi and Troitsky. Archive classification: math.OA Mathematics Subject Classification: 47L10, 47A15 Remarks: 15 pages, submitted to J. Operator Theory Submitted from: lacruz(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.4995 or http://arXiv.org/abs/1308.4995

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Abstract of a paper by Markus Passenbrunner
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Unconditionality of orthogonal spline systems in $L^p$" by Markus Passenbrunner. Abstract: Given any natural number $k$ and any dense point sequence $(t_n)$, we prove that the corresponding orthonormal spline system is an unconditional basis in reflexive $L^p$. Archive classification: math.FA Remarks: 33 pages Submitted from: markus.passenbrunner(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.5055 or http://arXiv.org/abs/1308.5055

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