March 2009 - Banach - mathdept.okstate.edu

Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "The number of weakly compact convex subsets of the Hilbert space" by Antonio Aviles. Abstract: We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k. Archive classification: math.GN math.FA Mathematics Subject Classification: 54B35, 52A07 Citation: Topology Appl. 155, No. 15, 1720-1725 (2008) The source file(s), Manyconvex.tex: 28889 bytes, is(are) stored in gzipped form as 0903.0163.gz with size 9kb. The corresponding postcript file has gzipped size 71kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0163 or http://arXiv.org/abs/0903.0163 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0163 or in gzipped form by using subject line get 0903.0163 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Renormings of the dual of James tree spaces" by Antonio Aviles. Abstract: We discuss renorming properties of the dual of a James tree space JT. We present examples of weakly Lindelof determined JT such that JT* admits neither strictly convex nor Kadec renorming and of weakly compactly generated JT such that JT* does not admit Kadec renorming although it is strictly convexifiable. Archive classification: math.FA Mathematics Subject Classification: 46B26 Citation: Bull. Lond. Math. Soc. 39, No. 2, 221-231 (2007) The source file(s), RosenthalLUR.tex: 41974 bytes, is(are) stored in gzipped form as 0903.0158.gz with size 13kb. The corresponding postcript file has gzipped size 91kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0158 or http://arXiv.org/abs/0903.0158 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0158 or in gzipped form by using subject line get 0903.0158 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Automatic norm continuity of weak* homeomorphisms" by Antonio Aviles. Abstract: We prove that in a certain class E of nonseparable Banach spaces the norm topology of the dual ball is definable in terms of its weak* topology. Thus, any weak* homeomorphism between duals balls of spaces in E is automatically norm-continuous. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26 Remarks: To appear in Houston J. Math The source file(s), weaknormH.tex: 27312 bytes, is(are) stored in gzipped form as 0903.0157.gz with size 8kb. The corresponding postcript file has gzipped size 67kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0157 or http://arXiv.org/abs/0903.0157 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0157 or in gzipped form by using subject line get 0903.0157 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "The unit ball of the Hilbert space in its weak topology" by Antonio Aviles. Abstract: We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when the space is nonseparable. Archive classification: math.GN math.FA Mathematics Subject Classification: 46B50, 46B26, 46C05, 54B30, 54D15. Citation: Proc. Am. Math. Soc. 135, No. 3, 833-836 (2007) The source file(s), HilbertBall.tex: 14810 bytes, is(are) stored in gzipped form as 0903.0154.gz with size 5kb. The corresponding postcript file has gzipped size 57kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0903.0154 or http://arXiv.org/abs/0903.0154 or by email in unzipped form by transmitting an empty message with subject line uget 0903.0154 or in gzipped form by using subject line get 0903.0154 to: math(a)arXiv.org.

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Abstract of a paper by Vladimir Kadets, Varvara Shepelska and Dirk Werner
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Thickness of the unit sphere, $\ell_1$-types, and the almost Daugavet property" by Vladimir Kadets, Varvara Shepelska and Dirk Werner. Abstract: We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give characterisations of this class of spaces in terms of $\ell_1$-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space $X$ is isomorphic to a space from this class if and only if $X$ contains an isomorphic copy of $\ell_1$. Archive classification: math.FA Mathematics Subject Classification: 46B04 Remarks: To appear in Houston Journal of Mathematics The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: werner(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.4503 or http://arXiv.org/abs/0902.4503 or by email in unzipped form by transmitting an empty message with subject line uget 0902.4503 or in gzipped form by using subject line get 0902.4503 to: math(a)arXiv.org.

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Abstract of a paper by Sonia Sharma
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Operator Spaces which are one-sided M-Ideals in their bidual" by Sonia Sharma. Abstract: We generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension property, Radon Nikod$\acute {\rm{y}}$m Property and many more, are retained in the non-commutative setting. We also discuss the dual setting of one-sided $L$-embedded operator spaces. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L07, 46B20, 46H10 Remarks: 17 pages The source file(s), sonia_paper.tex: 68819 bytes, is(are) stored in gzipped form as 0902.4257.gz with size 19kb. The corresponding postcript file has gzipped size 119kb. Submitted from: sonia(a)math.uh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.4257 or http://arXiv.org/abs/0902.4257 or by email in unzipped form by transmitting an empty message with subject line uget 0902.4257 or in gzipped form by using subject line get 0902.4257 to: math(a)arXiv.org.

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Abstract of a paper by R. Lechner
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "An interpolatory estimate for the UMD-valued directional Haar projection" by R. Lechner. Abstract: We establish an vector-valued interpolatory estimate between directional Haar projections and Riesz transforms. Archive classification: math.FA The source file(s), images/ring_domain--contained_in_cube.eps: 34448 bytes images/ring_domain--cubes_contained_in_covering.eps: 34423 bytes images/ring_domain--cubes_in_between.eps: 34072 bytes images/ring_domain.eps: 29005 bytes images/shifting_a_strip.eps: 57908 bytes main.bbl: 5508 bytes main.tex: 91054 bytes, is(are) stored in gzipped form as 0902.3597.tar.gz with size 69kb. The corresponding postcript file %has gzipped size 197kb. Submitted from: lechner(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.3597 or http://arXiv.org/abs/0902.3597 or by email in unzipped form by transmitting an empty message with subject line uget 0902.3597 or in gzipped form by using subject line get 0902.3597 to: math(a)arXiv.org.

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Abstract of a paper by M.I. Ostrovskii and V.S. Shulman
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Weak operator topology, operator ranges and operator equations via Kolmogorov widths" by M.I. Ostrovskii and V.S. Shulman. Abstract: Let $K$ be an absolutely convex infinite-dimensional compact in a Banach space $\mathcal{X}$. The set of all bounded linear operators $T$ on $\mathcal{X}$ satisfying $TK\supset K$ is denoted by $G(K)$. Our starting point is the study of the closure $WG(K)$ of $G(K)$ in the weak operator topology. We prove that $WG(K)$ contains the algebra of all operators leaving $\overline{\lin(K)}$ invariant. More precise results are obtained in terms of the Kolmogorov $n$-widths of the compact $K$. The obtained results are used in the study of operator ranges and operator equations. Archive classification: math.FA math.OA Mathematics Subject Classification: 47A05; 41A46; 47A30; 47A62 The source file(s), ostshu.tex: 68035 bytes, is(are) stored in gzipped form as 0902.3483.gz with size 21kb. The corresponding postcript file has gzipped size 139kb. Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.3483 or http://arXiv.org/abs/0902.3483 or by email in unzipped form by transmitting an empty message with subject line uget 0902.3483 or in gzipped form by using subject line get 0902.3483 to: math(a)arXiv.org.

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Abstract of a paper by Gines Lopez Perez
by alspach＠fourier.math.okstate.edu 06 Mar '09

06 Mar '09

This is an announcement for the paper "Banach spaces with many boundedly complete basic sequences failing PCP" by Gines Lopez Perez. Abstract: We prove that there exist Banach spaces not containing $\ell_1$, failing the point of continuity property and satisfying that every semi-normalized basic sequence has a boundedly complete basic subsequence. This answers in the negative the problem of the Remark 2 in H. P. Rosenthal. "Boundedly complete weak-Cauchy sequences in Banach spaces with PCP." J. Funct. Anal. 253 (2007) 772-781. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B22 The source file(s), pcp.tex: 25505 bytes, is(are) stored in gzipped form as 0902.3422.gz with size 8kb. The corresponding postcript file has gzipped size 72kb. Submitted from: glopezp(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0902.3422 or http://arXiv.org/abs/0902.3422 or by email in unzipped form by transmitting an empty message with subject line uget 0902.3422 or in gzipped form by using subject line get 0902.3422 to: math(a)arXiv.org.

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