Banach June 2014

banach@mathdept.okstate.edu

4 participants
26 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 Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "$\aleph$-injective Banach spaces and $\aleph$-projective compacta" by Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno. Abstract: A Banach space $E$ is said to be injective if for every Banach space $X$ and every subspace $Y$ of $X$ every operator $t:Y\to E$ has an extension $T:X\to E$. We say that $E$ is $\aleph$-injective (respectively, universally $\aleph$-injective) if the preceding condition holds for Banach spaces $X$ (respectively $Y$) with density less than a given uncountable cardinal $\aleph$. We perform a study of $\aleph$-injective and universally $\aleph$-injective Banach spaces which extends the basic case where $\aleph=\aleph_1$ is the first uncountable cardinal. When dealing with the corresponding ``isometric'' properties we arrive to our main examples: ultraproducts and spaces of type $C(K)$. We prove that ultraproducts built on countably incomplete $\aleph$-good ultrafilters are $(1,\aleph)$-injective as long as they are Lindenstrauss spaces. We characterize $(1,\aleph)$-injective $C(K)$ spaces as those in which the compact $K$ is an $F_\aleph$-space (disjoint open subsets which are the union of less than $\aleph$ many closed sets have disjoint closures) and we uncover some projectiveness properties of $F_\aleph$-spaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 54B30, 46B08, 54C15, 46B26 Remarks: This paper is to appear in Revista Matem\'atica Iberoamericana Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6733 or http://arXiv.org/abs/1406.6733

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Abstract of a paper by Jesus M. F. Castillo, Manuel Gonzalez and Pier Luigi Papini
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "On nested sequences of convex sets in a Banach space" by Jesus M. F. Castillo, Manuel Gonzalez and Pier Luigi Papini. Abstract: In this paper we study different aspects of the representation of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach space $X$ via a nested sequence of closed convex bounded sets of $X$. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: This paper is to appear in Studia Mathematica Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6725 or http://arXiv.org/abs/1406.6725

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Abstract of a paper by Felix Cabello Sanchez, Jesus M. F. Castillo and Nigel J. Kalton
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "Complex interpolation and twisted twisted Hilbert spaces" by Felix Cabello Sanchez, Jesus M. F. Castillo and Nigel J. Kalton. Abstract: We show that Rochberg's generalizared interpolation spaces $\mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to \mathscr Z^{(k)} \to 0$. We study some structural properties of those sequences; in particular, we show that nontriviality, having strictly singular quotient map, or having strictly cosingular embedding depend only on the basic case $n=k=1$. If we focus on the case of Hilbert spaces obtained from the interpolation scale of $\ell_p$ spaces, then $\mathscr Z^{(2)}$ becomes the well-known Kalton-Peck $Z_2$ space; we then show that $\mathscr Z^{(n)}$ is (or embeds in, or is a quotient of) a twisted Hilbert space only if $n=1,2$, which solves a problem posed by David Yost; and that it does not contain $\ell_2$ complemented unless $n=1$. We construct another nontrivial twisted sum of $Z_2$ with itself that contains $\ell_2$ complemented. Archive classification: math.FA Mathematics Subject Classification: 46M18, 46B70, 46B20 Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6723 or http://arXiv.org/abs/1406.6723

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Abstract of a paper by Javier Alejandro Chavez-Dominguez and Denka Kutzarova
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "Stability of low-rank matrix recovery and its connections to Banach space geometry" by Javier Alejandro Chavez-Dominguez and Denka Kutzarova. Abstract: There are well-known relationships between compressed sensing and the geometry of the finite-dimensional $\ell_p$ spaces. A result of Kashin and Temlyakov can be described as a characterization of the stability of the recovery of sparse vectors via $\ell_1$-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional $\ell_1$ and $\ell_2$ spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich proves an analogous relationship even for $\ell_p$ spaces with $p < 1$. In this paper we prove what we call matrix or noncommutative versions of these results: we characterize the stability of low-rank matrix recovery via Schatten $p$-(quasi-)norm minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional Schatten $p$-spaces. Archive classification: math.FA cs.IT math.IT Remarks: 19 pages, 1 figure Submitted from: jachavezd(a)math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6712 or http://arXiv.org/abs/1406.6712

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Abstract of a paper by Javier Alejandro Chavez-Dominguez
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "Lipschitz $p$-convex and $q$-concave maps" by Javier Alejandro Chavez-Dominguez. Abstract: The notions of $p$-convexity and $q$-concavity are mostly known because of their importance as a tool in the study of isomorphic properties of Banach lattices, but they also play a role in several results involving linear maps between Banach spaces and Banach lattices. In this paper we introduce Lipschitz versions of these concepts, dealing with maps between metric spaces and Banach lattices, and start by proving nonlinear versions of two well-known factorization theorems through $L_p$ spaces due to Maurey/Nikishin and Krivine. We also show that a Lipschitz map from a metric space into a Banach lattice is Lipschitz $p$-convex if and only if its linearization is $p$-convex. Furthermore, we elucidate why there is such a close relationship between the linear and nonlinear concepts by proving characterizations of Lipschitz $p$-convex and Lipschitz $q$-concave maps in terms of factorizations through $p$-convex and $q$-concave Banach lattices, respectively, in the spirit of the work of Raynaud and Tradacete. Archive classification: math.FA Remarks: 25 pages Submitted from: jachavezd(a)math.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.6357 or http://arXiv.org/abs/1406.6357

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Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "Tukey classification of some ideals in $\omega$ and the lattices of weakly compact sets in Banach spaces" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez. Abstract: We study the lattice structure of the family of weakly compact subsets of the unit ball $B_X$ of a separable Banach space $X$, equipped with the inclusion relation (this structure is denoted by $\mathcal{K}(B_X)$) and also with the parametrized family of almost inclusion relations $K \subseteq L+\epsilon B_X$, where $\epsilon>0$ (this structure is denoted by $\mathcal{AK}(B_X)$). Tukey equivalence between partially ordered sets and a suitable extension to deal with $\mathcal{AK}(B_X)$ are used. Assuming the axiom of analytic determinacy, we prove that separable Banach spaces fall into four categories, namely: $\mathcal{K}(B_X)$ is equivalent either to a singleton, or to $\omega^\omega$, or to the family $\mathcal{K}(\mathbb{Q})$ of compact subsets of the rational numbers, or to the family $[\mathfrak{c}]^{<\omega}$ of all finite subsets of the continuum. Also under the axiom of analytic determinacy, a similar classification of $\mathcal{AK}(B_X)$ is obtained. For separable Banach spaces not containing $\ell^1$, we prove in ZFC that $\mathcal{K}(B_X) \sim \mathcal{AK}(B_X)$ are equivalent to either $\{0\}$, $\omega^\omega$, $\mathcal{K}(\mathbb{Q})$ or $[\mathfrak{c}]^{<\omega}$. The lattice structure of the family of all weakly null subsequences of an unconditional basis is also studied. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B20(Primary), 03E60, 03E75, 06A06, 46B50, 03E75 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.5526 or http://arXiv.org/abs/1406.5526

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Abstract of a paper by Khalil Saadi
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "Some properties for Lipschitz strongly p-summing operators" by Khalil Saadi. Abstract: We consider the space of molecules endowed with the transpose version of the Chevet-Saphar norm and we identify its dual space with the space of Lipschitz strongly p-summing operators. We also extend some old results to the category of Lipschitz mappings and we give a factorization result of Lipschitz (p,r,s)-summing operators. Archive classification: math.FA Mathematics Subject Classification: [2000] 47B10, 46B28, 47L20 Remarks: 19 pages Submitted from: kh_saadi(a)yahoo.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.5551 or http://arXiv.org/abs/1406.5551

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Abstract of a paper by S. Astashkin, F. Sukochev, and D. Zanin
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p" by S. Astashkin, F. Sukochev, and D. Zanin. Abstract: Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B20, 46B09 Remarks: 14 pages, submitted Submitted from: astash(a)samsu.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.4950 or http://arXiv.org/abs/1406.4950

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Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg
by alspach＠math.okstate.edu 30 Jun '14

30 Jun '14

This is an announcement for the paper "A brief survey of Nigel Kalton's work on interpolation and related topics" by Michael Cwikel, Mario Milman and Richard Rochberg. Abstract: This is the third of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time, rather than concentrating on one particular paper, we attempt to give a general overview of Nigel's many contributions to the theory of interpolation of Banach spaces, and also, significantly, quasi-Banach spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 46B70, 46A16. Secondary 42B20, 42B30 Remarks: 11 pages Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.3842 or http://arXiv.org/abs/1406.3842

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Banach June 2014