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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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Abstract of a paper by Pandelis Dodos and Valentin Ferenczi
by Dale Alspach 19 May '06

19 May '06

This is an announcement for the paper "Some strongly bounded classes of Banach spaces" by Pandelis Dodos and Valentin Ferenczi. Abstract: We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach spaces. Archive classification: Functional Analysis Mathematics Subject Classification: 03E15; 46B03 Remarks: 10 pages The source file(s), DFversion18.tex: 27085 bytes, is(are) stored in gzipped form as 0605475.gz with size 9kb. The corresponding postcript file has gzipped size 52kb. Submitted from: ferenczi(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605475 or http://arXiv.org/abs/math.FA/0605475 or by email in unzipped form by transmitting an empty message with subject line uget 0605475 or in gzipped form by using subject line get 0605475 to: math(a)arXiv.org.

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CBMS conference on A Probabalistic and Combinatorial Approach in Analysis (second announcement)
by Artem Zvavitch 11 May '06

11 May '06

Dear Friends, This is the second announcement for the CBMS conference on 'A Probabilistic and Combinatorial Approach in Analysis', with Professor Mark Rudelson from the University of Missouri as the main speaker. The conference will be held at the Department of Mathematical Sciences of Kent State University in August 6-10 2006, followed by the conference on Analysis and Applications in August 11-12. We hope that you will be able to participate. Please, let us know as soon as possible if you are interested in attending. Please also find more information below: 1)With CBMS funding we will be able to cover the local expenses for most of the participants. We NEED to know if you wish to have a dormitory room. We hasten to mention that the dormitory is brand-spanking new, modern and, we expect, comfortable as well as conveniently located near to the site of the lectures. Please, let us know as soon as possible if you would prefer to stay in a hotel or need any other special housing arrangements. (This may require additional payment towards the housing costs.) 2) We NEED to know your travel arrangements; in particular, when are you arriving, by what means are you traveling and, if by air, PLEASE furnish us with complete details. The nearest airports are Cleveland Hopkins Airport (CLE) or Akron Canton Regional Airport (CAK). We wish to be sure to have someone at the correct airport to meet and greet you, take you to Kent, check you into your domicile, and help you settle in. 3) Along with this information we'll NEED to know how long you will be with us. Mark Rudelson's lectures are scheduled from August 6 at 11:00AM until August 10 at 4pm. You may check in to your room as early as August 5. On August 11-12 we will have additional lectures by participants and we welcome all of you to submit an abstract and title via e-mail as soon as possible. The check-out date for the dormitory rooms is August 13. 4) Please note that that breakfast and lunch will be provided by the conference, and we will send you a list of additional fun events and excitements in Kent and Cleveland soon. 5) All this information will be also provided on http://www.math.kent.edu/math/CBMS.cfm or, please contact Artem Zvavitch (zvavitch(a)math.kent.edu) for more information. Best Regards, Richard Aron, Joe Diestel, Per Enflo, Victor Lomonosov, Andrew Tonge, and Artem Zvavitch

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Abstract of a paper by Kusraev A.G. and Kutateladze S.S
by Dale Alspach 03 May '06

03 May '06

This is an announcement for the paper "Boolean methods in the theory of vector lattices" by Kusraev A.G. and Kutateladze S.S. Abstract: This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46 A 40 The source file(s), methods.lat: 131684 bytes, is(are) stored in gzipped form as 0605030.gz with size 38kb. The corresponding postcript file has gzipped size 123kb. Submitted from: sskut(a)member.ams.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605030 or http://arXiv.org/abs/math.FA/0605030 or by email in unzipped form by transmitting an empty message with subject line uget 0605030 or in gzipped form by using subject line get 0605030 to: math(a)arXiv.org.

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