Banach December 2009

banach@mathdept.okstate.edu

2 participants
8 discussions

Abstract of a paper by Mikko Kemppainen
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "On the Rademacher maximal function" by Mikko Kemppainen. Abstract: This paper studies a new maximal operator introduced by Hyt\"onen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L^p-boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to sigma-finite measure spaces with filtrations and the L^p-boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques are applied to prove that a weak type inequality is sufficient for L^p-boundedness and also to provide a characterization by concave functions. Archive classification: math.FA Mathematics Subject Classification: 46E40 (Primary); 42B25 (Secondary) Remarks: 22 pages, 4 figures The source file(s), RMF.bbl: 4575 bytes RMF.tex: 148459 bytes averages.pdf: 1054 bytes filtrations.pdf: 1394 bytes mart11.pdf: 1111 bytes mart33.pdf: 1082 bytes, is(are) stored in gzipped form as 0912.3358.tar.gz with size 39kb. The corresponding postcript file has gzipped size . Submitted from: mikko.k.kemppainen(a)helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.3358 or http://arXiv.org/abs/0912.3358 or by email in unzipped form by transmitting an empty message with subject line uget 0912.3358 or in gzipped form by using subject line get 0912.3358 to: math(a)arXiv.org.

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Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Some translation-invariant Banach function spaces which contain $c_0$" by Pascal Lefevre, Daniel Li, Herve Queffelec, and Luis Rodriguez-Piazza. Abstract: We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space $c_0$. Archive classification: math.FA Mathematics Subject Classification: MSC: Primary: 43A46, 46B20; Secondary: 42A55, 42B35, 43A07, 46E30 Citation: Studia Mathematica 163, 2 (2004) 137 - 155 The source file(s), LLQR3D.TEX: 56689 bytes, is(are) stored in gzipped form as 0912.3133.gz with size 18kb. The corresponding postcript file has gzipped size 109kb. Submitted from: daniel.li(a)euler.univ-artois.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.3133 or http://arXiv.org/abs/0912.3133 or by email in unzipped form by transmitting an empty message with subject line uget 0912.3133 or in gzipped form by using subject line get 0912.3133 to: math(a)arXiv.org.

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Abstract of a paper by Longyun Ding
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Borel reducibility and Holder($\alpha$) embeddability between Banach spaces" by Longyun Ding. Abstract: We investigate Borel reducibility between equivalence relations $E(X,p)=X^{\Bbb N}/\ell_p(X)$'s where $X$ is a separable Banach space. We show that this reducibility is related to the so called H\"older$(\alpha)$ embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between $E(L_r,p)$'s and $E(c_0,p)$'s for $r,p\in[1,+\infty)$. We also answer a problem presented by Kanovei in the affirmative by showing that $C({\Bbb R}^+)/C_0({\Bbb R}^+)$ is Borel bireducible to ${\Bbb R}^{\Bbb N}/c_0$. Archive classification: math.LO math.FA Mathematics Subject Classification: 03E15, 46B20, 47H99 Remarks: 29 pages The source file(s), Banach.tex: 57984 bytes, is(are) stored in gzipped form as 0912.1912.gz with size 16kb. The corresponding postcript file has gzipped size 128kb. Submitted from: dingly(a)nankai.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.1912 or http://arXiv.org/abs/0912.1912 or by email in unzipped form by transmitting an empty message with subject line uget 0912.1912 or in gzipped form by using subject line get 0912.1912 to: math(a)arXiv.org.

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Abstract of a paper by Ilijas Farah and Saharon Shelah
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "A dichotomy for the number of ultrapowers" by Ilijas Farah and Saharon Shelah. Abstract: We prove a strong dichotomy for the number of ultrapowers of a given countable model associated with nonprincipal ultrafilters on N. They are either all isomorphic, or else there are $2^{2^{\aleph_0}}$ many nonisomorphic ultrapowers. We prove the analogous result for metric structures, including C*-algebras and II$_1$ factors, as well as their relative commutants and include several applications. We also show that the C*-algebra B(H) always has nonisomorphic relative commutants in its ultrapowers associated with nonprincipal ultrafilters on N. Archive classification: math.LO math.OA Mathematics Subject Classification: 03C20, 46M07 Report Number: Shelah [FaSh:954] The source file(s), 2009i19-ultrapowers.tex: 122804 bytes, is(are) stored in gzipped form as 0912.0406.gz with size 33kb. The corresponding postcript file has gzipped size 176kb. Submitted from: ifarah(a)yorku.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.0406 or http://arXiv.org/abs/0912.0406 or by email in unzipped form by transmitting an empty message with subject line uget 0912.0406 or in gzipped form by using subject line get 0912.0406 to: math(a)arXiv.org.

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Abstract of a paper by Alon Ivtsan
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Stafney's lemma holds for several "classical" interpolation methods" by Alon Ivtsan. Abstract: Let (B_0,B_1) be a Banach pair. Stafney showed that in the definition of the norm in the Calderon complex interpolation method on the strip, one can replace the space F(B_0,B_1) with its subspace G(B_0,B_1) if the element belongs to the intersection of B_0 and B_1. We extend this result to a more general setting, which contains several well-known interpolation methods, namely the Calderon complex interpolation method on the annulus, an appropriate version of the Lions-Peetre real method, and the Peetre "plus minus" method. Archive classification: math.FA Mathematics Subject Classification: 46B70 (primary); 46B45 (secondary) Remarks: 7 pages The source file(s), stafney30-t.tex: 35607 bytes, is(are) stored in gzipped form as 0911.5719.gz with size 9kb. The corresponding postcript file has gzipped size 84kb. Submitted from: aloniv(a)tx.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5719 or http://arXiv.org/abs/0911.5719 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5719 or in gzipped form by using subject line get 0911.5719 to: math(a)arXiv.org.

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Abstract of a paper by W. Lawton
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "Minimal sequences and the Kadison-Singer problem" by W. Lawton. Abstract: The Kadison-Singer problem asks: does every pure state on the C$^*$-algebra $\ell^{\infty}(Z)$ admit a unique extension to the C$^*$-algebra $\cB(\ell^2(Z))$? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We prove that for measurable $S \subset \TT,$ $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k\in \ZZ}}$ is a finite union of Riesz sequences in $L^2(\TT)$ if and only if there exists a nonempty $\Lambda \subset \ZZ$ such that $\chi_{_\Lambda}$ is a minimal sequence and $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k \in \Lambda}}$ is a Riesz sequence. We also suggest some directions for future research. Archive classification: math.FA math.DS Mathematics Subject Classification: 37B10, 42A55, 46L05 Remarks: 10 pages, Theorem 1.1 was announced during conferences in St. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5559 or http://arXiv.org/abs/0911.5559 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5559 or in gzipped form by using subject line get 0911.5559 to: math(a)arXiv.org.

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Abstract of a paper by Rafa Espinola and Aurora Fernandez-Leon
by alspach＠fourier.math.okstate.edu 18 Dec '09

18 Dec '09

This is an announcement for the paper "On best proximity points in metric and Banach spaces" by Rafa Espinola and Aurora Fernandez-Leon. Abstract: In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We do it from two different approaches, leading each one of them to different results which complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with. Archive classification: math.FA math.MG Mathematics Subject Classification: 54H25, 47H09 Remarks: 17 pages. Accepted for publication in the Canadian Mathematical The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5263 or http://arXiv.org/abs/0911.5263 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5263 or in gzipped form by using subject line get 0911.5263 to: math(a)arXiv.org.

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conference in Cleveland
by Elisabeth Werner 17 Dec '09

17 Dec '09

CONFERENCE ON "PERSPECTIVES IN HIGH DIMENSIONS," CLEVELAND, AUGUST 1-7, 2010 This is an announcement of the conference on "Perspectives in High Dimensions," to be held on the campus of Case Western Reserve University in Cleveland, Ohio, U.S.A. from August 1 until August 7, 2010. The aim of the conference is to reflect on recent and future developments in broadly understood geometric functional analysis, with emphasis on interactions with other subfields of mathematics and with other mathematical sciences, including but not limited to computer science, mathematical physics and statistics. The scientific program will be set up under the guidance of the Scientific Committee consisting of Jean Bourgain Emmanuel Candes Persi Diaconis Boaz Klartag Stanislaw Szarek Santosh Vempala Roman Vershynin Elisabeth Werner The conference will be supported by the NSF via Focused Research Grant, which involves CWRU, Kent State University, University of Michigan and University of Missouri. We expect to be able to provide support to a substantial number of participants, with priority given to graduate students, junior researchers and to those lacking their own research funding, as well as to members of underrepresented groups. More details will be provided in the coming months. Should you have any questions, please contact one of the organizers (below), or check the temporary conference website at http://www.case.edu/artsci/math/perspectivesInHighDimensions/ Alexander Koldobsky (koldobskiya at missouri.edu) Mark Rudelson (rudelsonm at missouri.edu) Dmitry Ryabogin (ryabogin at math.kent.edu) Stanislaw Szarek (szarek at cwru.edu) Roman Vershynin (romanv at umich.edu) Elisabeth Werner (elisabeth.werner at case.edu) Artem Zvavitch (zvavitch at math.kent.edu) Local committee: Elizabeth Meckes (ese3 at cwru.edu) Mark Meckes (mark.meckes at case.edu) Dmitry Ryabogin (ryabogin at math.kent.edu) Stanislaw Szarek (szarek at cwru.edu) Elisabeth Werner (elisabeth.werner at case.edu) Artem Zvavitch (zvavitch at math.kent.edu)

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Banach December 2009