Banach September 2008

banach@mathdept.okstate.edu

1 participants
16 discussions

Abstract of a paper by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda
by alspach＠fourier.math.okstate.edu 29 Sep '08

29 Sep '08

This is an announcement for the paper "On dominated polynomials between Banach spaces" by Geraldo Botelho, Daniel Pellegrino and Pilar Rueda. Abstract: In this paper, among other results, we prove a conjecture concerning coincidence theorems for dominated polynomials. We also obtain an abstract version of Pietsch Domination Theorem (PDT) which unifies and generalizes several different nonlinear approaches; our result recovers, as a particular case, the well-known PDT for dominated multilinear mappings. Archive classification: math.FA Mathematics Subject Classification: 46B15; 46G25 Remarks: 10 pages The source file(s), conjecture19agosto2008-arxiv.tex: 34210 bytes, is(are) stored in gzipped form as 0809.4496.gz with size 10kb. The corresponding postcript file has gzipped size 85kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4496 or http://arXiv.org/abs/0809.4496 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4496 or in gzipped form by using subject line get 0809.4496 to: math(a)arXiv.org.

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Abstract of a paper by George Androulakis and Antoine Flattot
by alspach＠fourier.math.okstate.edu 29 Sep '08

29 Sep '08

This is an announcement for the paper "Hyperinvariant subspace for weighted composition operator on $L^p([0,1]^d)$" by George Androulakis and Antoine Flattot. Abstract: The main result of this paper is the existence of a hyperinvariant subspace of weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$, ($1 \leq p \leq \infty$) when the weight $v$ is in the class of ``generalized polynomials'' and the composition map is a bijective ergodic transform satisfying a given discrepancy. The work is based on the construction of a functional calculus initiated by Wermer and generalized by Davie. Archive classification: math.FA Mathematics Subject Classification: 47A15 ; 47A10; 47A60 The source file(s), WCO.tex: 48622 bytes, is(are) stored in gzipped form as 0809.4429.gz with size 14kb. The corresponding postcript file has gzipped size 122kb. Submitted from: giorgis(a)math.sc.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4429 or http://arXiv.org/abs/0809.4429 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4429 or in gzipped form by using subject line get 0809.4429 to: math(a)arXiv.org.

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Abstract of a paper by Geraldo Botelho and Daniel Pellegrino
by alspach＠fourier.math.okstate.edu 29 Sep '08

29 Sep '08

This is an announcement for the paper "Coincidences for multiple summing mappings" by Geraldo Botelho and Daniel Pellegrino. Abstract: In this note we prove new coincidence results for multiple summing mappings, related to the cotypes of the Banach spaces involved. Archive classification: math.FA Remarks: 3 pages, to appear in the resumes of the meeting ENAMA, Second The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.4171 or http://arXiv.org/abs/0809.4171 or by email in unzipped form by transmitting an empty message with subject line uget 0809.4171 or in gzipped form by using subject line get 0809.4171 to: math(a)arXiv.org.

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Abstract of a paper by Miguel Martin
by alspach＠fourier.math.okstate.edu 29 Sep '08

29 Sep '08

This is an announcement for the paper "The group of isometries of a Banach space and duality" by Miguel Martin. Abstract: We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples concerning numerical index, hermitian operators and dissipative operators are also shown. Archive classification: math.FA Mathematics Subject Classification: Primary: 46B04. Secondary: 46B10, 46E15, 47A12 Remarks: To appear in J. Funct. Anal. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3644 or http://arXiv.org/abs/0809.3644 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3644 or in gzipped form by using subject line get 0809.3644 to: math(a)arXiv.org.

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Abstract of a paper by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak
by alspach＠fourier.math.okstate.edu 29 Sep '08

29 Sep '08

This is an announcement for the paper "Banach spaces of bounded Szlenk index II" by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: For every $\alpha<\omega_1$ we establish the existence of a separable Banach space whose Szlenk index is $\omega^{\alpha\omega+1}$ and which is universal for all separable Banach spaces whose Szlenk-index does not exceed $\omega^{\alpha\omega}$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates. Archive classification: math.FA math.AG Mathematics Subject Classification: 46B20, 54H05 The source file(s), szlenkII_new.tex: 57543 bytes, is(are) stored in gzipped form as 0809.3626.gz with size 17kb. The corresponding postcript file has gzipped size 122kb. Submitted from: schlump(a)math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3626 or http://arXiv.org/abs/0809.3626 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3626 or in gzipped form by using subject line get 0809.3626 to: math(a)arXiv.org.

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Abstract of a paper by Tuomas Hytonen
by alspach＠fourier.math.okstate.edu 22 Sep '08

22 Sep '08

This is an announcement for the paper "The vector-valued non-homogeneous Tb theorem" by Tuomas Hytonen. Abstract: The paper gives a Banach space-valued extension of the ``$Tb$ theorem'' of Nazarov, Treil and Volberg (2003) concerning the boundedness of singular integral operators with respect to a measure $\mu$, which only satisfies an upper control on the size of balls. Under the same assumptions as in their result, such operators are shown to be bounded on the Bochner spaces $L^p(\mu;X)$ of functions with values in $X$ --- a Banach space with the unconditionality property of martingale differences (UMD) and a certain maximal function property, which holds for all typical examples of UMD spaces. The new proof deals directly with all $p\in(1,\infty)$ and relies on delicate estimates for the non-homogenous ``Haar'' functions, as well as McConnell's (1989) decoupling inequality for tangent martingale differences. Archive classification: math.FA math.CA Mathematics Subject Classification: 42B20;42B25; 46B09; 46E40; 60G46 Remarks: 40 pages, submitted for publication The source file(s), nonhomog.tex: 143196 bytes, is(are) stored in gzipped form as 0809.3097.gz with size 39kb. The corresponding postcript file has gzipped size 209kb. Submitted from: tuomas.hytonen(a)helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3097 or http://arXiv.org/abs/0809.3097 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3097 or in gzipped form by using subject line get 0809.3097 to: math(a)arXiv.org.

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Abstract of a paper by Detelin Dosev
by alspach＠fourier.math.okstate.edu 22 Sep '08

22 Sep '08

This is an announcement for the paper "Commutators on $\ell_1$" by Detelin Dosev. Abstract: The main result is that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17) to obtain this result and use this generalization to obtain partial results about the commutators on spaces $\X$ which can be represented as $\displaystyle \X\simeq \left ( \bigoplus_{i=0}^{\infty} \X\right)_{p}$ for some $1\leq p<\infty$ or $p=0$. In particular, it is shown that every compact operator on $L_1$ is a commutator. A characterization of the commutators on $\ell_{p_1}\oplus\ell_{p_2}\oplus\cdots\oplus\ell_{p_n}$ is given. We also show that strictly singular operators on $\linf$ are commutators. Archive classification: math.FA Mathematics Subject Classification: 47B47 Remarks: 17 pages. Submitted to the Journal of Functional Analysis The source file(s), Commutators_l1.tex: 58728 bytes, is(are) stored in gzipped form as 0809.3047.gz with size 16kb. The corresponding postcript file has gzipped size 110kb. Submitted from: ddosev(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3047 or http://arXiv.org/abs/0809.3047 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3047 or in gzipped form by using subject line get 0809.3047 to: math(a)arXiv.org.

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Abstract of a paper by S. R. Cowell and N. J. Kalton
by alspach＠fourier.math.okstate.edu 22 Sep '08

22 Sep '08

This is an announcement for the paper "Asymptotic unconditionality" by S. R. Cowell and N. J. Kalton. Abstract: We show that a separable real Banach space embeds almost isometrically in a space $Y$ with a shrinking 1-unconditional basis if and only if $\lim_{n \to \infty} \|x^* + x_n^*\| = \lim_{n \to \infty} \|x^* - x_n^*\|$ whenever $x^* \in X^*$, $(x_n^*)$ is a weak$^*$-null sequence and both limits exist. If $X$ is reflexive then $Y$ can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng. Archive classification: math.FA Mathematics Subject Classification: 46B03; 46B20 Remarks: 26 pages. Submitted for publication. This is a replacement The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.2294 or http://arXiv.org/abs/0809.2294 or by email in unzipped form by transmitting an empty message with subject line uget 0809.2294 or in gzipped form by using subject line get 0809.2294 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles, Vladimir Kadets, Miguel Martin, Javier Meri, and Varvara Shepelska
by alspach＠fourier.math.okstate.edu 22 Sep '08

22 Sep '08

This is an announcement for the paper "Slicely countably determined Banach spaces. Applications to the Daugavet and the alternative Daugavet equations" by Antonio Aviles, Vladimir Kadets, Miguel Martin, Javier Meri, and Varvara Shepelska. Abstract: We introduce the class of slicely countably determined Banach spaces which contains in particular all spaces with the RNP and all spaces without copies of $\ell_1$. We present many examples and several properties of this class. We give some applications to Banach spaces with the Daugavet and the alternative Daugavet properties, lush spaces and Banach spaces with numerical index $1$. In particular, we show that the dual of a real infinite-dimensional Banach with the alternative Daugavet property contains $\ell_1$ and that operators which do not fix copies of $\ell_1$ on a space with the alternative Daugavet property satisfy the alternative Daugavet equation. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20. Secondary 46B03, 46B04, 46B22, 47A12 The source file(s), AvilesKadetsMartinMeriShepelska.tex: 107489 bytes, is(are) stored in gzipped form as 0809.2723.gz with size 30kb. The corresponding postcript file has gzipped size 172kb. Submitted from: mmartins(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.2723 or http://arXiv.org/abs/0809.2723 or by email in unzipped form by transmitting an empty message with subject line uget 0809.2723 or in gzipped form by using subject line get 0809.2723 to: math(a)arXiv.org.

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Abstract of a paper by Christoph Haberl and Franz E. Schuster
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "General Lp affine isoperimetric inequalities" by Christoph Haberl and Franz E. Schuster. Abstract: Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality. Archive classification: math.DG math.FA Mathematics Subject Classification: 52A40; 52A39 The source file(s), Lpaffine.tex: 76896 bytes, is(are) stored in gzipped form as 0809.1995.gz with size 20kb. The corresponding postcript file has gzipped size 116kb. Submitted from: franz.schuster(a)tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1995 or http://arXiv.org/abs/0809.1995 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1995 or in gzipped form by using subject line get 0809.1995 to: math(a)arXiv.org.

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Banach September 2008