December 2014 - 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 Brendan Pass and Susanna Spektor
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "On Khinchine type inequalities for pairwise independent Rademacher random variables" by Brendan Pass and Susanna Spektor. Abstract: We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ pairwise independent Rademacher random variables. We establish that an analogue of Khintchine's inequality cannot hold in this setting with a constant that is independent of $N$; in fact, we prove that the best constant one can hope for is at least $N^{1/2-1/p}$. Furthermore, we show that this estimate is sharp for exchangeable vectors when $p = 4$. As a fortunate consequence of our work, we obtain similar results for $3$-wise independent vectors. Archive classification: math.FA math.PR Submitted from: sanaspek(a)yandex.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.7859 or http://arXiv.org/abs/1412.7859

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Abstract of a paper by Mikhail I. Ostrovskii and Beata Randrianantoanina
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "Metric spaces admitting low-distortion embeddings into all $n$-dimensional Banach spaces" by Mikhail I. Ostrovskii and Beata Randrianantoanina. Abstract: For a fixed $K\gg 1$ and $n\in\mathbb{N}$, $n\gg 1$, we study metric spaces which admit embeddings with distortion $\le K$ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $\log n$-dimensional Euclidean spaces, and equilateral spaces. We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that any $n$-point ultrametric can be embedded with uniformly bounded distortion into any Banach space of dimension $\log n$. The main result of the paper is a new example of a family of finite metric spaces which are not metric compositions of classical examples and which do embed with uniformly bounded distortion into any Banach space of dimension $n$. This partially answers a question of G.~Schechtman. Archive classification: math.FA math.MG Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12, 30L05, 46B15, 52A21 Remarks: 35 pages, 4 figures Submitted from: randrib(a)miamioh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.7670 or http://arXiv.org/abs/1412.7670

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Abstract of a paper by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "On operator relations between locally convex spaces" by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul. Abstract: A linear operator $T:X \to Y$ between vector spaces is called strictly singular if for any infinite dimensional closed vector subspace $M$ of $X$, the restriction of $T$ on $M$ is not a topological isomorphism. In this note we introduced some sufficient conditions on domain and range spaces such that any bounded linear operator in between is strictly singular, and give some examples of spaces satisfying these conditions. Archive classification: math.FA Remarks: 15 pages, presented in the context of 8th Australian and New The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5761 or http://arXiv.org/abs/1412.5761

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Abstract of a paper by Karl-Mikael Perfekt
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "On M-ideals and o-O type spaces" by Karl-Mikael Perfekt. Abstract: We consider pairs of Banach spaces (M_0, M) such that M_0 is defined in terms of a little-o condition, and M is defined by the corresponding big-O condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, M\"obius invariant spaces of analytic functions, Lipschitz-H\"older spaces, etc. It has previously been shown that the bidual M_0** of M_0 is isometrically isomorphic with M. The main result of this paper is that M_0 is an M-ideal in M. This has several useful consequences: M_0 has Pelczynskis properties (u) and (V), M_0 is proximinal in M, and M_0* is a strongly unique predual of M, while M_0 itself never is a strongly unique predual. Archive classification: math.FA Remarks: 9 pages Submitted from: karlmikp(a)math.ntnu.no The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5486 or http://arXiv.org/abs/1412.5486

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Abstract of a paper by Liran Rotem
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "A letter: The log-Brunn-Minkowski inequality for complex bodies" by Liran Rotem. Abstract: In this short note we explain why the log-Brunn-Minkowski conjecture is correct for complex convex bodies. We do this by relating the conjecture to the notion of complex interpolation, and appealing to a general theorem by Cordero-Erausquin. Archive classification: math.MG math.FA Submitted from: liranro1(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5321 or http://arXiv.org/abs/1412.5321

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Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "Almost sure-sign convergence of Hardy-type Dirichlet series" by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris. Abstract: Hartman proved in 1939 that the width of the largest possible strip in the complex plane, on which a Dirichlet series $\sum_n a_n n^{-s}$ is uniformly a.s.-sign convergent (i.e., $\sum_n \varepsilon_n a_n n^{-s}$ converges uniformly for almost all sequences of signs $\varepsilon_n =\pm 1$) but does not convergent absolutely, equals $1/2$. We study this result from a more modern point of view within the framework of so called Hardy-type Dirichlet series with values in a Banach space. Archive classification: math.FA Mathematics Subject Classification: 30B50, 30H10, 46G20 Submitted from: dcarando(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.5030 or http://arXiv.org/abs/1412.5030

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Abstract of a paper by Peide Liu and Maofa Wang
by alspach＠math.okstate.edu 30 Dec '14

30 Dec '14

This is an announcement for the paper "Burkholder-Gundy-Davis inequality in martingale Hardy spaces with variable exponent" by Peide Liu and Maofa Wang. Abstract: In this paper, the classical Dellacherie's theorem about stochastic process is extended to variable exponent Lebesgue spaces. As its applications, we obtain variable exponent analogues of several famous inequalities in classical martingale theory, including convexity lemma, Burkholder-Gundy-Davis' inequality and Chevalier's inequality. Moreover, we investigate some other equivalent relations between variable exponent martingale Hardy spaces. Archive classification: math.FA Submitted from: pdliu(a)whu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.8146 or http://arXiv.org/abs/1412.8146

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Abstract of a paper by Eusebio Gardella and Hannes Thiel
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

This is an announcement for the paper "Quotients of Banach algebras acting on $L^p$-spaces" by Eusebio Gardella and Hannes Thiel. Abstract: We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study of Banach algebras generated by invertible isometries of $L^p$-spaces. Archive classification: math.OA math.FA Mathematics Subject Classification: Primary: 47L10, 43A15. Secondary: 46J10 Remarks: 7 pages Submitted from: gardella(a)uoregon.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.3985 or http://arXiv.org/abs/1412.3985

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Abstract of a paper by Tomasz Kania
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

This is an announcement for the paper "On C*-algebras which cannot be decomposed into tensor products with factors infinite-dimensional" by Tomasz Kania. Abstract: We prove that C*-algebras which satisfy a Banach-space property of being a Grothendieck space cannot be decomposed into a tensor product of two infinite-dimensional Banach spaces. By a result of Pfitzner, this class contains all von Neumann algebras and their norm-quotients. We thus strengthen a recent result of Ghasemi who established a similar conclusion for C*-tensor products in the case of SAW*-algebras. In particular, we solve in the negative a problem of Simon Wassermann concerning tensorial decompositions of the Calkin algebra in the category of Banach spaces. Archive classification: math.OA math.FA Submitted from: tomasz.marcin.kania(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1412.3621 or http://arXiv.org/abs/1412.3621

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