January 2009 - Banach - mathdept.okstate.edu

Abstract of a paper by Marius Junge and Javier Parcet
by alspach＠fourier.math.okstate.edu 15 Jan '09

15 Jan '09

This is an announcement for the paper "Maurey's factorization theory for operator spaces" by Marius Junge and Javier Parcet. Abstract: We provide an operator space version of Maurey's factorization theorem. The main tool is an embedding result of independent interest. Applications for operator spaces and noncommutative Lp spaces are included. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L07; 47B10 Remarks: 26 pages The source file(s), Maurey.tex: 91710 bytes, is(are) stored in gzipped form as 0901.1928.gz with size 28kb. The corresponding postcript file has gzipped size 160kb. Submitted from: javier.parcet(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.1928 or http://arXiv.org/abs/0901.1928 or by email in unzipped form by transmitting an empty message with subject line uget 0901.1928 or in gzipped form by using subject line get 0901.1928 to: math(a)arXiv.org.

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Abstract of a paper by Markus Kunze
by alspach＠fourier.math.okstate.edu 15 Jan '09

15 Jan '09

This is an announcement for the paper "A general Pettis integral and applications to transition semigroups" by Markus Kunze. Abstract: Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we prove conditions ensuring that a semigroup consisting of kernel operators is Laplace transformable such that the Laplace transform consists of kernel operators again. Archive classification: math.FA Mathematics Subject Classification: 46G10, 47D03, 60J35 Remarks: 19 pages, no figures The source file(s), pettists.tex: 64277 bytes, is(are) stored in gzipped form as 0901.1771.gz with size 19kb. The corresponding postcript file has gzipped size 122kb. Submitted from: m.c.kunze(a)tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.1771 or http://arXiv.org/abs/0901.1771 or by email in unzipped form by transmitting an empty message with subject line uget 0901.1771 or in gzipped form by using subject line get 0901.1771 to: math(a)arXiv.org.

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Abstract of a paper by Piotr Koszmider, Miguel Martin and Javier Meri
by alspach＠fourier.math.okstate.edu 15 Jan '09

15 Jan '09

This is an announcement for the paper "Isometries on extremely non-complex Banach spaces" by Piotr Koszmider, Miguel Martin and Javier Meri . Abstract: We construct an example of a real Banach space whose group of surjective isometries reduces to $\pm\Id$, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup. To do so, we present examples of extremely non-complex Banach spaces (i.e.\ spaces $X$ such that $\|\Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$ on $X$) which are not of the form $C(K)$, and we study the surjective isometries on this class of Banach spaces. Archive classification: math.FA math.OA Mathematics Subject Classification: Primary: 46B04. Secondary: 46B10, 46B20, 46E15, 47A99 Remarks: 20 pages The source file(s), KoszmiderMartinMeri.tex: 84147 bytes, is(are) stored in gzipped form as 0901.1512.gz with size 24kb. The corresponding postcript file has gzipped size 138kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.1512 or http://arXiv.org/abs/0901.1512 or by email in unzipped form by transmitting an empty message with subject line uget 0901.1512 or in gzipped form by using subject line get 0901.1512 to: math(a)arXiv.org.

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Abstract of a paper by Christoph Kriegler and Christian Le Merdy
by alspach＠fourier.math.okstate.edu 11 Jan '09

11 Jan '09

This is an announcement for the paper "Tensor extension properties of C(K)-representations and applications to unconditionality" by Christoph Kriegler and Christian Le Merdy. Abstract: Let K be any compact set. The C^*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept of R-boundedness. Then we apply these results to operators with a uniformly bounded H^\infty-calculus, as well as to unconditionality on L^p. We show that any unconditional basis on L^p `is' an unconditional basis on L^2 after an appropriate change of density. Archive classification: math.OA math.FA Mathematics Subject Classification: 47A60; 46B28 The source file(s), CK-Art.tex: 73146 bytes, is(are) stored in gzipped form as 0901.1025.gz with size 22kb. The corresponding postcript file has gzipped size 145kb. Submitted from: clemerdy(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.1025 or http://arXiv.org/abs/0901.1025 or by email in unzipped form by transmitting an empty message with subject line uget 0901.1025 or in gzipped form by using subject line get 0901.1025 to: math(a)arXiv.org.

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Abstract of a paper by George Androulakis, Alexey I. Popov, Adi Tcaciuc and Vladimir G. Troitsky
by alspach＠fourier.math.okstate.edu 11 Jan '09

11 Jan '09

This is an announcement for the paper "Almost invariant half-spaces of operators on Banach spaces" by George Androulakis, Alexey I. Popov, Adi Tcaciuc and Vladimir G. Troitsky. Abstract: We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators on l_p (1 \le p < \infty) or c_0. Archive classification: math.FA Mathematics Subject Classification: 47A15 Remarks: 13 pages The source file(s), invariantV9.tex: 38986 bytes, is(are) stored in gzipped form as 0901.0752.gz with size 12kb. The corresponding postcript file has gzipped size 95kb. Submitted from: vtroitsky(a)math.ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.0752 or http://arXiv.org/abs/0901.0752 or by email in unzipped form by transmitting an empty message with subject line uget 0901.0752 or in gzipped form by using subject line get 0901.0752 to: math(a)arXiv.org.

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Abstract of a paper by Petr Hajek, Gilles Lancien and Antonin Prochazka
by alspach＠fourier.math.okstate.edu 11 Jan '09

11 Jan '09

This is an announcement for the paper "Weak$^*$ dentability index of spaces $C([0,\alpha])$" by Petr Hajek, Gilles Lancien and Antonin Prochazka. Abstract: We compute the weak$^*$-dentability index of the spaces $C(K)$ where $K$ is a countable compact space. Namely $\mbox{Dz}(C([0,\omega^{\omega^\alpha}])) = \omega^{1+\alpha+1}$, whenever $0\le\alpha<\omega_1$. More generally, $\mbox{Dz}(C(K))=\omega^{1+\alpha+1}$ if $K$ is a scattered compact whose height $\eta(K)$ satisfies $\omega^\alpha<\eta(K)\leq \omega^{\alpha+1}$ with an $\alpha$ countable. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B03, 46E15 The source file(s), delta4revised.tex: 28188 bytes, is(are) stored in gzipped form as 0901.0681.gz with size 9kb. The corresponding postcript file has gzipped size 78kb. Submitted from: protony(a)centrum.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.0681 or http://arXiv.org/abs/0901.0681 or by email in unzipped form by transmitting an empty message with subject line uget 0901.0681 or in gzipped form by using subject line get 0901.0681 to: math(a)arXiv.org.

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Abstract of a paper by Antonis Manoussakis and Anna Maria Pelczar
by alspach＠fourier.math.okstate.edu 11 Jan '09

11 Jan '09

This is an announcement for the paper "Quasiminimality in mixed Tsirelson spaces" by Antonis Manoussakis and Anna Maria Pelczar. Abstract: We prove that mixed Tsirelson spaces T[(M_n,\theta_n)_n], where M_n=A_n for all n or M_n=S_n for all n, are quasiminimal. We prove that under certain assumptions on the sequence (\theta_n)_n the dual spaces are also quasiminimal. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B45 Remarks: 25 pages The source file(s), quasiminimality.tex: 87433 bytes, is(are) stored in gzipped form as 0812.4711.gz with size 26kb. The corresponding postcript file has gzipped size 163kb. Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.4711 or http://arXiv.org/abs/0812.4711 or by email in unzipped form by transmitting an empty message with subject line uget 0812.4711 or in gzipped form by using subject line get 0812.4711 to: math(a)arXiv.org.

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Abstract of a paper by V. P. Fonf, R. J. Smith and S. Troyanski
by alspach＠fourier.math.okstate.edu 11 Jan '09

11 Jan '09

This is an announcement for the paper "A note on fragmentability and weak-G_delta sets" by V. P. Fonf, R. J. Smith and S. Troyanski. Abstract: In terms of fragmentability, we describe a new class of Banach spaces which do not contain weak-G_delta open bounded subsets. In particular, none of these spaces is isomorphic to a separable polyhedral space. Archive classification: math.FA The source file(s), frag-w-gdelta6.tex: 18701 bytes, is(are) stored in gzipped form as 0812.4690.gz with size 7kb. The corresponding postcript file has gzipped size 70kb. Submitted from: smith(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.4690 or http://arXiv.org/abs/0812.4690 or by email in unzipped form by transmitting an empty message with subject line uget 0812.4690 or in gzipped form by using subject line get 0812.4690 to: math(a)arXiv.org.

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