Banach

banach@mathdept.okstate.edu

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 15 May '08

15 May '08

This is an announcement for the paper "On classes of Banach spaces admitting ``small" universal spaces" by Pandelis Dodos. Abstract: We characterize those classes $\ccc$ of separable Banach spaces admitting a separable universal space $Y$ (that is, a space $Y$ containing, up to isomorphism, all members of $\ccc$) which is not universal for all separable Banach spaces. The characterization is a byproduct of the fact, proved in the paper, that the class $\mathrm{NU}$ of non-universal separable Banach spaces is strongly bounded. This settles in the affirmative the main conjecture form \cite{AD}. Our approach is based, among others, on a construction of $\llll_\infty$-spaces, due to J. Bourgain and G. Pisier. As a consequence we show that there exists a family $\{Y_\xi:\xi<\omega_1\}$ of separable, non-universal, $\llll_\infty$-spaces which uniformly exhausts all separable Banach spaces. A number of other natural classes of separable Banach spaces are shown to be strongly bounded as well. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B03, 46B07, 46B15 Remarks: 25 pages, no figures The source file(s), Universal-ArXiv.tex: 81806 bytes, is(are) stored in gzipped form as 0805.2043.gz with size 24kb. The corresponding postcript file has gzipped size 143kb. Submitted from: pdodos(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2043 or http://arXiv.org/abs/0805.2043 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2043 or in gzipped form by using subject line get 0805.2043 to: math(a)arXiv.org.

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 15 May '08

15 May '08

This is an announcement for the paper "On antichains of spreading models of Banach spaces" by Pandelis Dodos. Abstract: We show that for every separable Banach space $X$, either $\spw(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\spw(X)$ contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell and B. Sari. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B20 Remarks: 14 pages, no figures. Canadian Mathematical Bulletin (to appear) The source file(s), SP-ArXiv.tex: 44752 bytes, is(are) stored in gzipped form as 0805.2038.gz with size 13kb. The corresponding postcript file has gzipped size 96kb. Submitted from: pdodos(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2038 or http://arXiv.org/abs/0805.2038 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2038 or in gzipped form by using subject line get 0805.2038 to: math(a)arXiv.org.

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 15 May '08

15 May '08

This is an announcement for the paper "Definability under duality" by Pandelis Dodos. Abstract: It is shown that if $A$ is an analytic class of separable Banach spaces with separable dual, then the set $A^*=\{ Y:\exists X\in A \text{ with } Y\cong X^*\}$ is analytic. The corresponding result for pre-duals is false. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E15, 46B10 Remarks: 9 pages, no figures The source file(s), DualsVersion-ArXiv.tex: 29048 bytes, is(are) stored in gzipped form as 0805.2036.gz with size 9kb. The corresponding postcript file has gzipped size 79kb. Submitted from: pdodos(a)math.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.2036 or http://arXiv.org/abs/0805.2036 or by email in unzipped form by transmitting an empty message with subject line uget 0805.2036 or in gzipped form by using subject line get 0805.2036 to: math(a)arXiv.org.

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Abstract of a paper by Pandelis Dodos, Jordi Lopez Abad and Stevo Todorcevic
by alspach＠fourier.math.okstate.edu 15 May '08

15 May '08

This is an announcement for the paper "Unconditional basic sequences in spaces of large density" by Pandelis Dodos, Jordi Lopez Abad and Stevo Todorcevic. Abstract: We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement that every Banach space of density $\aleph_\omega$ contains an unconditional basic sequence. Archive classification: math.FA math.LO Mathematics Subject Classification: 46B03, 03E35 The source file(s), DLT.tex: 74305 bytes, is(are) stored in gzipped form as 0805.1860.gz with size 22kb. The corresponding postcript file has gzipped size 136kb. Submitted from: abad(a)logique.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.1860 or http://arXiv.org/abs/0805.1860 or by email in unzipped form by transmitting an empty message with subject line uget 0805.1860 or in gzipped form by using subject line get 0805.1860 to: math(a)arXiv.org.

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Abstract of a paper by Oscar Blasco and Sandra Pott
by alspach＠fourier.math.okstate.edu 13 May '08

13 May '08

This is an announcement for the paper "Embeddings between operator-valued dyadic BMO spaces" by Oscar Blasco and Sandra Pott. Abstract: We investigate a scale of dyadic operator-valued BMO spaces, corresponding to the different yet equivalent characterizations of dyadic BMO in the scalar case. In the language of operator spaces, we investigate different operator space structures on the scalar dyadic BMO space which arise naturally from the different characterisations of scalar BMO. We also give sharp dimensional growth estimates for the sweep of functions and its bilinear extension in some of those different dyadic BMO spaces. Archive classification: math.FA Mathematics Subject Classification: Primary 42B30, 42B35, Secondary 47B35 Remarks: to appear in Illinois J. Math The source file(s), BlascoPott2.tex: 45114 bytes, is(are) stored in gzipped form as 0805.0620.gz with size 14kb. The corresponding postcript file has gzipped size 102kb. Submitted from: s.pott(a)maths.gla.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0805.0620 or http://arXiv.org/abs/0805.0620 or by email in unzipped form by transmitting an empty message with subject line uget 0805.0620 or in gzipped form by using subject line get 0805.0620 to: math(a)arXiv.org.

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symposium
by Dale Alspach 05 May '08

05 May '08

On May 27-28 the Institute of Mathematics of the Hebrew University of Jerusalem is organizing a memorial symposium for Lior Tzafriri, titled "Geometry of Banach Spaces". A tentative program of the symposium can be found on the webpage: http://www.ma.huji.ac.il/~landau/conf/banach_08.html

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Abstract of a paper by Michael Doree, Olga Maleva
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "A compact null set containing a differentiability point of every Lipschitz function" by Michael Doree and Olga Maleva. Abstract: We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly. Archive classification: math.FA math.CA Mathematics Subject Classification: 46G05; 46T20 Remarks: 31 pages The source file(s), DoreMaleva.tex: 76535 bytes, is(are) stored in gzipped form as 0804.4576.gz with size 22kb. The corresponding postcript file has gzipped size 144kb. Submitted from: o.maleva(a)warwick.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.4576 or http://arXiv.org/abs/0804.4576 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4576 or in gzipped form by using subject line get 0804.4576 to: math(a)arXiv.org.

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Abstract of a paper by Jarno Talponen
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "The isometry group of L^{p}(\mu,\X) is SOT-contractible" by Jarno Talponen. Abstract: We will show that if (\Omega,\Sigma,\mu) is an atomless positive measure space, X is a Banach space and 1\leq p<\infty, then the group of isometric automorphisms on the Bochner space L^{p}(\mu,X) is contractible in the strong operator topology. We do not require \Sigma or X above to be separable. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B25; 46E40 The source file(s), contr32.tex: 27449 bytes, is(are) stored in gzipped form as 0804.4427.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.4427 or http://arXiv.org/abs/0804.4427 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4427 or in gzipped form by using subject line get 0804.4427 to: math(a)arXiv.org.

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Abstract of a paper by Andrea Colesanti and Eugenia Saorin-Gomez
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals" by Andrea Colesanti and Eugenia Saorin-Gomez. Abstract: We use Brunn-Minkowski inequalities for quermassintegrals to deduce a family of inequalities of Poincar\'e type on the unit sphere and on the boundary of smooth convex bodies in the $n$-dimensional Euclidean space. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20; 26D10 Remarks: 15 pages The source file(s), cs3.tex: 37802 bytes, is(are) stored in gzipped form as 0804.3867.gz with size 12kb. The corresponding postcript file has gzipped size 109kb. Submitted from: colesant(a)math.unifi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3867 or http://arXiv.org/abs/0804.3867 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3867 or in gzipped form by using subject line get 0804.3867 to: math(a)arXiv.org.

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Abstract of a paper by Matthew Daws, Hung Le Pham and Stuart White
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" by Matthew Daws, Hung Le Pham and Stuart White. Abstract: We investigate possible preduals of the measure algebra $M(G)$ of a locally compact group and the Fourier algebra $A(G)$ of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak$^*$-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals $C_0(G)$ of $M(G)$ and $C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a natural coassociative multiplication and show that the canonical predual gives rise to the unique weak$^*$-topology making both the multiplication separately weak$^*$-continuous and the coassociative multiplication weak$^*$-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure. Archive classification: math.FA math.OA Mathematics Subject Classification: 43A20, 43A77 Remarks: 21 pages The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are) stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding postcript file has gzipped size 133kb. Submitted from: matt.daws(a)cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3764 or http://arXiv.org/abs/0804.3764 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3764 or in gzipped form by using subject line get 0804.3764 to: math(a)arXiv.org.

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