Banach

banach@mathdept.okstate.edu

2549 discussions

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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Abstract of a paper by Elisabeth Werner and Deping Ye
by alspach＠fourier.math.okstate.edu 29 Dec '08

29 Dec '08

This is an announcement for the paper "Inequalities for mixed $p$-affine surface area" by Elisabeth Werner and Deping Ye. Abstract: We prove new Alexandrov-Fenchel type inequalities and new affine isoperimetric inequalities for mixed $p$-affine surface areas. We introduce a new class of bodies, the illumination surface bodies, and establish some of their properties. We show, for instance, that they are not necessarily convex. We give geometric interpretations of $L_p$ affine surface areas, mixed $p$-affine surface areas and other functionals via these bodies. The surprising new element is that not necessarily convex bodies provide the tool for these interpretations. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20, 53A15 Remarks: 39 pages The source file(s), MixedLp.tex: 97032 bytes, is(are) stored in gzipped form as 0812.4550.gz with size 26kb. The corresponding postcript file has gzipped size 162kb. Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.4550 or http://arXiv.org/abs/0812.4550 or by email in unzipped form by transmitting an empty message with subject line uget 0812.4550 or in gzipped form by using subject line get 0812.4550 to: math(a)arXiv.org.

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Abstract of a paper by Kenneth R. Davidson and Alex Wright
by alspach＠fourier.math.okstate.edu 29 Dec '08

29 Dec '08

This is an announcement for the paper "Operator algebras with unique preduals" by Kenneth R. Davidson and Alex Wright. Abstract: We show that every free semigroup algebras has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak*-closed unital operator operator algebra containing a weak* dense subalgebra of compact operators has a unique Banach space predual. Archive classification: math.OA math.FA Mathematics Subject Classification: 47L50; 46B04; 47L35 Remarks: 13 pages The source file(s), DavidsonWright3a.tex: 44578 bytes, is(are) stored in gzipped form as 0812.3159.gz with size 14kb. The corresponding postcript file has gzipped size 96kb. Submitted from: krdavids(a)uwaterloo.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.3159 or http://arXiv.org/abs/0812.3159 or by email in unzipped form by transmitting an empty message with subject line uget 0812.3159 or in gzipped form by using subject line get 0812.3159 to: math(a)arXiv.org.

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Abstract of a paper by Roman Vershynin
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "Spectral norm of products of random and deterministic matrices" by Roman Vershynin. Abstract: We study the spectral norm of matrices M that can be factored as M=BA, where A is a random matrix with independent mean zero entries, and B is a fixed matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show that the spectral norm of such an m by n matrix M is bounded by \sqrt{m} + \sqrt{n}, which is sharp. In other words, in regard to the spectral norm, products of random and deterministic matrices behave similarly to random matrices with independent entries. This result along with the previous work of M. Rudelson and the author implies that the smallest singular value of a random m times n matrix with i.i.d. mean zero entries and bounded (4+epsilon)-th moment is bounded below by \sqrt{m} - \sqrt{n-1} with high probability. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52; 46B09 Remarks: 34 pages, no figures The source file(s), product-random-deterministic.tex: 81516 bytes, is(are) stored in gzipped form as 0812.2432.gz with size 22kb. The corresponding postcript file has gzipped size 147kb. Submitted from: romanv(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2432 or http://arXiv.org/abs/0812.2432 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2432 or in gzipped form by using subject line get 0812.2432 to: math(a)arXiv.org.

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Abstract of a paper by Robin Nittka
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "On a new type concept for Banach spaces" by Robin Nittka. Abstract: In order to measure qualitative properties we introduce a new notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. As an application we give a new proof that certain classical Banach spaces are non-isomorphic. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 7 pages The source file(s), type.bbl: 1571 bytes type.tex: 27062 bytes, is(are) stored in gzipped form as 0812.2216.tar.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. Submitted from: robin.nittka(a)uni-ulm.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.2216 or http://arXiv.org/abs/0812.2216 or by email in unzipped form by transmitting an empty message with subject line uget 0812.2216 or in gzipped form by using subject line get 0812.2216 to: math(a)arXiv.org.

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Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda
by alspach＠fourier.math.okstate.edu 16 Dec '08

16 Dec '08

This is an announcement for the paper "Factorization theorems for dominated polynomials" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However, this alternative scheme is shown not to be satisfactory until the equivalence is proved. Archive classification: math.FA Mathematics Subject Classification: 46G25 The source file(s), II-Factorization2dic08.tex: 15703 bytes, is(are) stored in gzipped form as 0812.1401.gz with size 5kb. The corresponding postcript file has gzipped size 62kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0812.1401 or http://arXiv.org/abs/0812.1401 or by email in unzipped form by transmitting an empty message with subject line uget 0812.1401 or in gzipped form by using subject line get 0812.1401 to: math(a)arXiv.org.

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