Banach June 2006

banach@mathdept.okstate.edu

2 participants
9 discussions

Abstract of a paper by Michael Cwikel and Svante Janson
by Dale Alspach 23 Jun '06

23 Jun '06

This is an announcement for the paper "Complex interpolation of compact operators mapping into the couple (FL^{\infty},FL_{1}^{\infty})" by Michael Cwikel and Svante Janson. Abstract: If (A_0,A_1) and (B_0,B_1) are Banach couples and a linear operator T from A_0 + A_1 to B_0 + B_1 maps A_0 compactly into B_0 and maps A_1 boundedly into B_1, does T necessarily also map [A_0,A_1]_s compactly into [B_0,B_1]_s for s in (0,1)? After 42 years this question is still not answered, not even in the case where T is also compact from A_1 to B_1. But affirmative answers are known for many special choices of (A_0,A_1) and (B_0,B_1). Furthermore it is known that it would suffice to resolve this question in the special case where (B_0,B_1) is the special couple (l^\infty(FL^\infty), l^\infty(FL^\infty_1)). Here FL^\infty is the space of all sequences which are Fourier coefficients of bounded functions, FL^\infty_1 is the weighted space of all sequences (a_n) such that (e^n a_n) is in FL^\infty, and thus B_0 and B_1 are the spaces of bounded sequences of elements in these spaces (i.e., they are spaces of doubly indexed sequences). We provide an affirmative answer to this question in the related but simpler case where (B_0,B_1) is the special couple (FL^\infty,FL^\infty_1). Archive classification: Functional Analysis Mathematics Subject Classification: 46B70 Remarks: 21 pages The source file(s), sj192.tex: 81719 bytes, is(are) stored in gzipped form as 0606551.gz with size 22kb. The corresponding postcript file has gzipped size 106kb. Submitted from: svante.janson(a)math.uu.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606551 or http://arXiv.org/abs/math.FA/0606551 or by email in unzipped form by transmitting an empty message with subject line uget 0606551 or in gzipped form by using subject line get 0606551 to: math(a)arXiv.org.

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Banach space theory - Last announcement
by Félix Cabello Sánchez 22 Jun '06

22 Jun '06

Dear colleague, this is the last announcement of the Satellite conference of the world congress ICM2006: Banach space theory: classical topics and new directions http://www.banachspaces.com The conference aim is to contemplate the topic of Banach spaces from an open and broader point of view; so, in addition to classical Banach space theory, related topics of active research have been included. There will be a special session on Polynomials on Banach spaces organized by R. Aron, D. García and M. Maestre. The main lines of the conference can thus be described as: ·Structure and geometry of infinite dimensional Banach and quasi-Banach spaces ·Infinite dimensional topology ·Asymptotic geometric analysis ·Categorical and homological methods ·Applications of descriptive set theory ·Polynomials on Banach spaces The list of main speakers includes so far: S. Argyros, National Technical University, Athens, Greece J. Bastero, Universidad de Zaragoza, Zaragoza, Spain F. Bombal, Universidad Complutense, Madrid, Spain G. Godefroy, Université Paris 6, Paris, France N.J. Kalton, University of Missouri, Columbia (Missouri), USA J. Lindenstrauss, The Hebrew University of Jerusalem, Jerusalem, Israel V. Milman, University of Tel Aviv, Tel Aviv, Israel A. Naor, Microsoft Research, Redmond (Washington), USA J. Orihuela, Universidad de Murcia, Murcia, Spain A. Rodríguez-Palacios, Universidad de Granada, Granada, Spain S. Szarek, Case Western Reserve University, Cleveland (Ohio), USA E. Odell, University of Texas, Austin (Texas), USA M. Valdivia, Universidad de Valencia, Valencia, Spain General information about the conference Place. The conference will take place in Cáceres, in the Complejo Cultural San Francisco, from 4 to 8 September, 2006. Registration. The ordinary registration fee is 100 EUR. For students, there is a reduced fee of 50 EUR. There is also a combined offer that includes catering and accommodation. See Combined offer to read about it. Catering. You are offered the possibility of getting a ticket that allows you to have breakfast and lunch (not dinner) from 4 to 8 September. Price is 80 EUR. There is also a combined offer that includes registration fee and accommodation. See Combined offer to read about it. Accommodation. There is the possibility of housing at the Residence Diego Muñoz Torrero, placed in front of the site of the conference. Price is 30 EUR per day and person in double room. There is also a combined offer that includes registration fee and catering. See Combined offer to read about it. Of course, you can choose to look for your own accommodation. A list of some hotels appears in the conference web-site. Combined offer. You can choose a combined offer registration that includes: registration fee, accommodation at the Residence Diego Muñoz Torrero, and catering (breakfast and lunch, not dinner) during the conference, for a total of 300 EUR. Invited lectures. It is intended that in the mornings there will take place the invited lectures by the main speakers. Contributed talks. In the evenings, there will be sessions of contributed talks of 15-30 min. People willing to deliver a talk are encouraged to send an abstract using the proper form at the web site. Deadline for submission of abstracts is July 15, 2006. Thematic sessions. There is the possibility to group contributed talks in thematic sessions. People interested in organizing such sessions should send a proposal to the contact address of the organization. Proceedings. The proceedings of the conference shall be published in the journal Extracta Mathematicae. The deadline for submissin of abstracts is 21 December 2006. History of Banach Space Conferences. Since 1996, the Department of Mathematics of the University of Extremadura organizes, at even years, a Banach Spaces conferece in either Badajoz or Cáceres. The proceedings of Conferences I-IV have appeared in Extracta Mathematicae and can be found at http://www.unex.es/extracta/extracta.html. The proceedings of the V Conference will be published by the Cambridge University Press as a volume in the Lecture Notes Series of the London Mathematical Society. All the information about the V Conference (Cáceres, 2004) and its proceedings can be found at http://www.banachspaces.com/banach04 Scientific Committee W.B. Johnson, Texas A&M University, College Station (Texas), USA J. Lindenstrauss, The Hebrew University of Jerusalem, Jerusalem, Israel B. Maurey, Université Paris 7, Paris, France A. Pajor, Université de Marne-la-Vallée, Marne-la-Vallée, France A. Pelczynski, Polish Academy of Sciences, Warsawa, Poland D. Preiss, University College London, London, UK N. Tomczak-Jaegermann, University of Alberta, Edmonton (Alberta), Canada J.M.F. Castillo, Universidad de Extremadura, Badajoz, Spain -- Banach space theory: classical topics & new directions

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Abstract of a paper by S. J. Dilworth, E. Odell, Th. Schlumprecht, and Andras Zsak
by Dale Alspach 14 Jun '06

14 Jun '06

This is an announcement for the paper "Coefficient quantization in Banach spaces" by S. J. Dilworth, E. Odell, Th. Schlumprecht, and Andras Zsak. Abstract: Let (e_i) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a `finite alphabet'. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c_0. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 41A65 Remarks: LaTeX, 28 pages The source file(s), dosz042106-arXiv.tex: 95960 bytes, is(are) stored in gzipped form as 0606317.gz with size 27kb. The corresponding postcript file has gzipped size 118kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606317 or http://arXiv.org/abs/math.FA/0606317 or by email in unzipped form by transmitting an empty message with subject line uget 0606317 or in gzipped form by using subject line get 0606317 to: math(a)arXiv.org.

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Abstract of a paper by Mathieu Meyer and Shlomo Reisner
by Dale Alspach 14 Jun '06

14 Jun '06

This is an announcement for the paper "Shadow systems and volume of polar convex bodies" by Mathieu Meyer and Shlomo Reisner. Abstract: We prove that the reciprocal of the volume of the polar bodies, about the Santal\'o point, of a {\em shadow system\/} of convex bodies $K_t$, is a convex function of $t$. Thus extending to the non-symmetric case a result of Campi and Gronchi. The case that the reciprocal of the volume is an affine function of $t$ is also investigated and is characterized under certain conditions. We apply these results to prove exact reverse Santal\'o inequality for polytopes in $\rd{d}$ that have at most $d+3$ vertices. Archive classification: Functional Analysis Remarks: to appear in Mathematika The source file(s), MMSR.tex: 55818 bytes, is(are) stored in gzipped form as 0606305.gz with size 18kb. The corresponding postcript file has gzipped size 93kb. Submitted from: reisner(a)math.haifa.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606305 or http://arXiv.org/abs/math.FA/0606305 or by email in unzipped form by transmitting an empty message with subject line uget 0606305 or in gzipped form by using subject line get 0606305 to: math(a)arXiv.org.

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Abstract of a paper by Eugene Ostrovsky and Leonid Sirota
by Dale Alspach 07 Jun '06

07 Jun '06

This is an announcement for the paper "Some new moment rearrangement invariant spaces; theory and applications" by Eugene Ostrovsky and Leonid Sirota. Abstract: In this article we introduce and investigate some new Banach spaces, so - called moment spaces, and consider applications to the Fourier series, singular integral operators, theory of martingales. Archive classification: Functional Analysis Mathematics Subject Classification: Primary (1991) 37B30,33K55 The source file(s), MOMSPC1.tex: 56149 bytes, is(are) stored in gzipped form as 0605732.gz with size 18kb. The corresponding postcript file has gzipped size 72kb. Submitted from: leos(a)post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605732 or http://arXiv.org/abs/math.FA/0605732 or by email in unzipped form by transmitting an empty message with subject line uget 0605732 or in gzipped form by using subject line get 0605732 to: math(a)arXiv.org.

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Abstract of a paper by Zsolt Pales and Vera Zeidan
by Dale Alspach 03 Jun '06

03 Jun '06

This is an announcement for the paper "Generalized Jacobian for functions with infinite dimensional range and domain" by Zsolt P\'ales and Vera Zeidan. Abstract: In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikod\'ym property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the $\beta$-compactness, the $\beta$-upper semicontinuity, and a mean-value theorem. A connection with known notions is provided and chain rules are proved using key results developed. This included the vectorization and restriction theorem, and the extension theorem. Therefore, the generalized Jacobian introduced in this paper is proved to enjoy all the properties required of a derivative like-set. Archive classification: Functional Analysis Mathematics Subject Classification: 49J52 The source file(s), gen-jacobian3a.tex: 25440 bytes, is(are) stored in gzipped form as 0605771.gz with size 9kb. The corresponding postcript file has gzipped size 39kb. Submitted from: zeidan(a)math.msu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605771 or http://arXiv.org/abs/math.FA/0605771 or by email in unzipped form by transmitting an empty message with subject line uget 0605771 or in gzipped form by using subject line get 0605771 to: math(a)arXiv.org.

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Abstract of a paper by Oliver Dragicevic, Stefanie Petermichl, and Alexander Volberg
by Dale Alspach 03 Jun '06

03 Jun '06

This is an announcement for the paper "Sharp estimates of martingale transforms in higher dimensions and applications to the Ahlfors-Beurling operator" by Oliver Dragicevic, Stefanie Petermichl, and Alexander Volberg. Abstract: The main aspiration of this note is to construct several different Haar-type systems in euclidean spaces of higher dimensions and prove sharp Lp bounds for the corresponding martingale transforms. In dimension one this was a result of Burkholder. The motivation for working in this direction is the search for Lp estimates of the Ahlfors-Beurling operator. Archive classification: Functional Analysis Remarks: 41 pages, 12 figures The source file(s), Fbeds.tex: 100688 bytes, is(are) stored in gzipped form as 0606006.gz with size 31kb. The corresponding postcript file has gzipped size 121kb. Submitted from: oliver.dragicevic(a)fmf.uni-lj.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0606006 or http://arXiv.org/abs/math.FA/0606006 or by email in unzipped form by transmitting an empty message with subject line uget 0606006 or in gzipped form by using subject line get 0606006 to: math(a)arXiv.org.

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Abstract of a paper by Vladimir Kadets, Miguel Martin, and Rafael Paya
by Dale Alspach 01 Jun '06

01 Jun '06

This is an announcement for the paper "Recent progress and open questions on the numerical index of Banach spaces" by Vladimir Kadets, Miguel Martin, and Rafael Paya . Abstract: The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 47A12 Remarks: 27 pages, 4 figures, to appear in RACSAM The source file(s), KaMaPa.tex: 98692 bytes, adp.eps: 35617 bytes, dp.eps: 34093 bytes, lush.eps: 26434 bytes, norm.eps: 11837 bytes, is(are) stored in gzipped form as 0605781.tar.gz with size 66kb. The corresponding postcript file has gzipped size 167kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605781 or http://arXiv.org/abs/math.FA/0605781 or by email in unzipped form by transmitting an empty message with subject line uget 0605781 or in gzipped form by using subject line get 0605781 to: math(a)arXiv.org.

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Abstract of a paper by S.V. Konyagin and L. Vesely
by Dale Alspach 01 Jun '06

01 Jun '06

This is an announcement for the paper "Decomposable quadratic forms in Banach spaces" by S.V. Konyagin and L. Vesely. Abstract: A continuous quadratic form on a real Banach space $X$ is called {\em decomposable} if it is the difference of two nonnegative (i.e., positively semidefinite) continuous quadratic forms. We prove that if $X$ belongs to a certain class of superreflexive Banach spaces, including all $L_p(\mu)$ spaces with $2\le p<\infty$, then each continuous quadratic form on $X$ is decomposable. On the other hand, on each infinite-dimensional $L_1(\mu)$ space there exists a continuous quadratic form $q$ that is not delta-convex (i.e., $q$ is not representable as difference of two continuous convex functions); in particular, $q$ is not decomposable. Related results concerning delta-convexity are proved and some open problems are stated. Archive classification: Functional Analysis Mathematics Subject Classification: 46B99 (Primary) 52A41, 15A63 (Secondary) Remarks: 11 pages The source file(s), KonyaginVesely.tex: 32898 bytes, birkmult.cls: 53923 bytes, is(are) stored in gzipped form as 0605549.tar.gz with size 26kb. The corresponding postcript file has gzipped size 56kb. Submitted from: Libor.Vesely(a)mat.unimi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605549 or http://arXiv.org/abs/math.FA/0605549 or by email in unzipped form by transmitting an empty message with subject line uget 0605549 or in gzipped form by using subject line get 0605549 to: math(a)arXiv.org.

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Banach June 2006