Banach February 2006

banach@mathdept.okstate.edu

1 participants
8 discussions

Abstract of a paper by Wieslaw Kubis
by Dale Alspach 28 Feb '06

28 Feb '06

This is an announcement for the paper "Linearly ordered compacta and Banach spaces with a projectional resolution of the identity" by Wieslaw Kubis. Abstract: We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a Valdivia compact and every separable subspace of $C(K)$ is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: Primary: 46B03, 46B26; Secondary: 54F05, 46E15, 54C35 Remarks: 13 pages The source file(s), cmplmntn_property6.tex: 45742 bytes, is(are) stored in gzipped form as 0602628.gz with size 14kb. The corresponding postcript file has gzipped size 66kb. Submitted from: wkubis(a)pu.kielce.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0602628 or http://arXiv.org/abs/math.FA/0602628 or by email in unzipped form by transmitting an empty message with subject line uget 0602628 or in gzipped form by using subject line get 0602628 to: math(a)arXiv.org.

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Abstract of a paper by Boris Rubin
by Dale Alspach 27 Feb '06

27 Feb '06

This is an announcement for the paper "Generalized cosine transforms and classes of star bodies" by Boris Rubin. Abstract: The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry. Archive classification: Functional Analysis; Differential Geometry Mathematics Subject Classification: 44A12 The source file(s), an_red.tex: 66611 bytes, is(are) stored in gzipped form as 0602540.gz with size 22kb. The corresponding postcript file has gzipped size 100kb. Submitted from: borisr(a)math.lsu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0602540 or http://arXiv.org/abs/math.FA/0602540 or by email in unzipped form by transmitting an empty message with subject line uget 0602540 or in gzipped form by using subject line get 0602540 to: math(a)arXiv.org.

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Abstract of a paper by Olvido Delgado and Javier Soria
by Dale Alspach 23 Feb '06

23 Feb '06

This is an announcement for the paper "Optimal domain for the Hardy operator" by Olvido Delgado and Javier Soria. Abstract: We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a $\delta$-ring. A precise description is given for the case of the minimal Lorentz spaces. Archive classification: Functional Analysis; Classical Analysis and ODEs Mathematics Subject Classification: 46E30, 46B25 Remarks: 15 pages The source file(s), DeSo.tex: 40756 bytes, is(are) stored in gzipped form as 0602426.gz with size 13kb. The corresponding postcript file has gzipped size 66kb. Submitted from: soria(a)ub.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0602426 or http://arXiv.org/abs/math.FA/0602426 or by email in unzipped form by transmitting an empty message with subject line uget 0602426 or in gzipped form by using subject line get 0602426 to: math(a)arXiv.org.

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Abstract of a paper by Bernhard Haak, Jan van Neerven and Mark Veraar
by Dale Alspach 23 Feb '06

23 Feb '06

This is an announcement for the paper "A stochastic Datko-Pazy theorem" by Bernhard Haak, Jan van Neerven and Mark Veraar. Abstract: Let $H$ be a Hilbert space and $E$ a Banach space. In this note we present a sufficient condition for an operator $R: H\to E$ to be $\ga$--radonifying in terms of Riesz sequences in $H$. This result is applied to recover a result of Lutz Weis and the second named author on the $R$-boundedness of resolvents, which is used to obtain a Datko-Pazy type theorem for the stochastic Cauchy problem. We also present some perturbation results. Archive classification: Functional Analysis Mathematics Subject Classification: 47D06; 28C20; 46B09; 46B15; 47N30 Remarks: 10 pages The source file(s), Haak-vanNeerven-Veraar-arxiv.tex: 33344 bytes, is(are) stored in gzipped form as 0602427.gz with size 10kb. The corresponding postcript file has gzipped size 60kb. Submitted from: bernhard.haak(a)math.uni-karlsruhe.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0602427 or http://arXiv.org/abs/math.FA/0602427 or by email in unzipped form by transmitting an empty message with subject line uget 0602427 or in gzipped form by using subject line get 0602427 to: math(a)arXiv.org.

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Abstract of a paper by G. Androulakis and K. Beanland
by Dale Alspach 02 Feb '06

02 Feb '06

This is an announcement for the paper "A hereditarily indecomposable asymptotic $\ell_2$ Banach space" by G. Androulakis and K. Beanland. Abstract: A Hereditarily Indecomposable asymptotic $\ell_2$ Banach space is constructed. The existence of such a space answers a question of B. Maurey and verifies a conjecture of W.T. Gowers. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 46B03 Remarks: 29 pages The source file(s), HIHilbert.tex: 98830 bytes, is(are) stored in gzipped form as 0601778.gz with size 25kb. The corresponding postcript file has gzipped size 139kb. Submitted from: kjbeanland(a)smcm.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0601778 or http://arXiv.org/abs/math.FA/0601778 or by email in unzipped form by transmitting an empty message with subject line uget 0601778 or in gzipped form by using subject line get 0601778 to: math(a)arXiv.org.

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Abstract of a paper by Michel Talagrand
by Dale Alspach 31 Jan '06

31 Jan '06

This is an announcement for the paper "Maharam's problem" by Michel Talagrand. Abstract: We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947). Archive classification: Functional Analysis Mathematics Subject Classification: 28A12 The source file(s), s1.TEX: 75873 bytes, is(are) stored in gzipped form as 0601689.gz with size 23kb. The corresponding postcript file has gzipped size 105kb. Submitted from: spinglass(a)talagrand.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0601689 or http://arXiv.org/abs/math.FA/0601689 or by email in unzipped form by transmitting an empty message with subject line uget 0601689 or in gzipped form by using subject line get 0601689 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge, Christian Le Merdy and Quanhua Xu
by Dale Alspach 31 Jan '06

31 Jan '06

This is an announcement for the paper "$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces" by Marius Junge, Christian Le Merdy and Quanhua Xu. Abstract: In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, $q$-Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 47A60; Secondary 46L55, 46L69 Remarks: 118 pages The source file(s), JLX.tex: 355560 bytes (looks big), is(are) stored in gzipped form as 0601645.gz with size 94kb. The corresponding postcript file has gzipped size 394kb. Submitted from: qx(a)math.univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0601645 or http://arXiv.org/abs/math.FA/0601645 or by email in unzipped form by transmitting an empty message with subject line uget 0601645 or in gzipped form by using subject line get 0601645 to: math(a)arXiv.org.

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Abstract of a paper by Pavel Shvartsman
by Dale Alspach 31 Jan '06

31 Jan '06

This is an announcement for the paper "On extensions of Sobolev functions defined on regular subsets of metric measure spaces" by Pavel Shvartsman. Abstract: We characterize the restrictions of first order Sobolev functions to regular subsets of a homogeneous metric space and prove the existence of the corresponding linear extension operator. Archive classification: Functional Analysis Mathematics Subject Classification: 46E35 The source file(s), SobolevExtension.tex: 96827 bytes, is(are) stored in gzipped form as 0601679.gz with size 18kb. The corresponding postcript file has gzipped size 80kb. Submitted from: pshv(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0601679 or http://arXiv.org/abs/math.FA/0601679 or by email in unzipped form by transmitting an empty message with subject line uget 0601679 or in gzipped form by using subject line get 0601679 to: math(a)arXiv.org.

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Banach February 2006