Banach

banach@mathdept.okstate.edu

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Abstract of a paper by Stephan Fackler
by alspach＠math.okstate.edu 21 Jul '14

21 Jul '14

This is an announcement for the paper "Regularity properties of sectorial operators: counterexamples and open problems" by Stephan Fackler. Abstract: We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples. Archive classification: math.FA Mathematics Subject Classification: 47D06 (Primary) 47A60, 35K90 (Secondary) Remarks: 21 pages Submitted from: stephan.fackler(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.1142 or http://arXiv.org/abs/1407.1142

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Abstract of a paper by Slawomir Borzdynski and Andrzej Wisnicki
by alspach＠math.okstate.edu 21 Jul '14

21 Jul '14

This is an announcement for the paper "A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings" by Slawomir Borzdynski and Andrzej Wisnicki. Abstract: It is shown that if $S$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E$, then the set of common fixed points of $S$ is a nonempty nonexpansive retract of $C$. This partially solves a long-standing open problem in metric fixed point theory in the case of commutative semigroups. Archive classification: math.FA Submitted from: awisnic(a)hektor.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1407.0359 or http://arXiv.org/abs/1407.0359

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Abstract of a paper by Said Amana Abdillah, Jean Esterle, andBernhard Hermann Haak
by alspach＠math.okstate.edu 21 Jul '14

21 Jul '14

This is an announcement for the paper "Sur quelques extensions au cadre Banachique de la notion d'op\'erateur de Hilbert-Schmidt" by Said Amana Abdillah, Jean Esterle, and Bernhard Hermann Haak. Abstract: In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing operators, $\gamma$-summing or $\gamma$-radonifying operators, weakly $*1$-nuclear operators and classes of operators defined via factorization properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt operators as the class of all operators $u:E\to F$ such that $w\circ u \circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\to E$ and every bounded operator $w:F\to H_2$, where $H_1$ et $H_2$ are Hilbert spaces. Besides the trivial case where one of the spaces $E$ or $F$ is a "Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces $E$ or $F$ is a Hilbert space. Archive classification: math.FA Remarks: 18 pages Submitted from: bernhard.haak(a)math.u-bordeaux1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1406.7546 or http://arXiv.org/abs/1406.7546

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SUMIRFAS 2014
by Bill Johnson 21 Jul '14

21 Jul '14

2nd ANNOUNCEMENT OF SUMIRFAS 2014 The Summer Informal Regional Functional Analysis Seminar July 25-27 Texas A&M University, College Station The speakers for SUMIRFAS 2014 are March Boedihardjo A new characterization of certain quasidiagonal operators Michael Brannan L_p -representations of discrete quantum groups and exotic quantum group C*-algebras Caleb Eckhardt Unitary representations of nilpotent groups and the structure of the C*-algebras they generate Matthew Kennedy Boundaries of reduced C*-algebras of discrete groups Vern Paulsen Quantum chromatic numbers Gilles Pisier A continuum of C*-norms on B(H)?B(H) and related tensor products Lova Randrianarivony TBA Dan Voiculsecu Some C*-algebras which are coronas of non-C*-Banach algebras Deping Ye Is Einstein's "spooky action" common? The webpage for SUMIRFAS, including links to the schedule and abstracts, can be found at http://www.math.tamu.edu/~kerr/workshop/sumirfas2014 The first talk will be at 2:00 pm on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 166. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html SUMIRFAS will be preceded by a Concentration Week on Free Probability from July 21 to 25. Topics will include operator algebras, the connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The webpage is located at: http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. For information about the Concentration Week on Free Probability contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema <ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu>.

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SUMIRFAS 2014
by Bill Johnson 02 Jul '14

02 Jul '14

1st ANNOUNCEMENT OF SUMIRFAS 2014 The Summer Informal Regional Functional Analysis Seminar July 25-27 Texas A&M University, College Station The speakers for SUMIRFAS 2014 are March Boedihardjo Gilles Pisier Michael Brannan Lova Randrianarivony Caleb Eckhardt Dan Voiculescu Matthew Kennedy Deping Ye Vern Paulsen The schedule for SUMIRFAS will be posted on the Workshop in Analysis and Probability webpage: http://www.math.tamu.edu/~kerr/workshop The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 166. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html Coffee and refreshments will be available in Blocker 148. SUMIRFAS will be preceded by a Concentration Week on Free Probability from July 21 to 25. Topics will include operator algebras, the connections to random matrix theory, operator-valued and fully matricial techniques, stochastic processes, limit theorems, and free stochastic differential equations. The program will feature lecture series by Greg Anderson, Serban Belinschi, and Dimitri Shlyakhtenko. The webpage is located at: http://www.math.tamu.edu/~jwilliams/Free_Probability_2014 The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. For information about the Concentration Week on Free Probability contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema <ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu>.

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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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