- Banach - mathdept.okstate.edu

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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Abstract of a paper by Ioannis Gasparis
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "New examples of $c_0$-saturated Banach spaces II" by Ioannis Gasparis. Abstract: For every Banach space $Z$ with a shrinking unconditional basis satisfying upper $p$-estimates for some $p > 1$, an isomorphically polyhedral Banach space is constructed having an unconditional basis and admitting a quotient isomorphic to $Z$. Archive classification: math.FA Mathematics Subject Classification: 46B03 The source file(s), satur2.tex: 36833 bytes, is(are) stored in gzipped form as 0809.1815.gz with size 11kb. The corresponding postcript file has gzipped size 93kb. Submitted from: ioagaspa(a)math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1815 or http://arXiv.org/abs/0809.1815 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1815 or in gzipped form by using subject line get 0809.1815 to: math(a)arXiv.org.

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Abstract of a paper by Ioannis Gasparis
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "New examples of $c_0$-saturated Banach spaces" by Ioannis Gasparis. Abstract: For every $ 1 < p < \infty $ an isomorphically polyhedral Banach space $E_p$ is constructed having an unconditional basis and admitting a quotient isomorphic to $\ell_p$. It is also shown that $E_p$ is not isomorphic to a subspace of a $C(K)$ space for every countable and compact metric space $K$. Archive classification: math.FA Mathematics Subject Classification: 46B03 The source file(s), satur.tex: 82312 bytes, is(are) stored in gzipped form as 0809.1808.gz with size 22kb. The corresponding postcript file has gzipped size 143kb. Submitted from: ioagaspa(a)math.auth.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1808 or http://arXiv.org/abs/0809.1808 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1808 or in gzipped form by using subject line get 0809.1808 to: math(a)arXiv.org.

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Abstract of a paper by Jarno Talponen
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "Special symmetries of Banach spaces isomorphic to Hilbert spaces" by Jarno Talponen. Abstract: In this paper Hilbert spaces are characterized among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical here: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space. Archive classification: math.FA Mathematics Subject Classification: 46C15; 46B04 The source file(s), SSNSb.tex: 30955 bytes, is(are) stored in gzipped form as 0809.1789.gz with size 9kb. The corresponding postcript file has gzipped size 74kb. Submitted from: talponen(a)cc.helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1789 or http://arXiv.org/abs/0809.1789 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1789 or in gzipped form by using subject line get 0809.1789 to: math(a)arXiv.org.

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Abstract of a paper by Fulvio Ricci and Joan Verdera
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "Duality in spaces of finite linear combinations of atoms" by Fulvio Ricci and Joan Verdera. Abstract: In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0<p\leq 1$ on ${\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on $(p,\infty)$-atoms, $0<p < 1$, whose analogue for $p=1$ is known to be false. Let $0 < p <1$ and let $T$ be a linear operator defined on the space of finite linear combinations of $(p,\infty)$-atoms, $0<p < 1 $, which takes values in a Banach space $B$. If $T$ is uniformly bounded on $(p,\infty)$-atoms, then $T$ extends to a bounded operator from $H^p({\mathbb R}^n)$ into $B$. Archive classification: math.FA Mathematics Subject Classification: 42B30 Remarks: 15 pages The source file(s), atoms.tex: 40423 bytes, is(are) stored in gzipped form as 0809.1719.gz with size 14kb. The corresponding postcript file has gzipped size 101kb. Submitted from: fricci(a)sns.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.1719 or http://arXiv.org/abs/0809.1719 or by email in unzipped form by transmitting an empty message with subject line uget 0809.1719 or in gzipped form by using subject line get 0809.1719 to: math(a)arXiv.org.

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Abstract of a paper by Zoltan Kannai
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "Uniform convergence for convexification of dominated pointwise convergent continuous functions" by Zoltan Kannai. Abstract: The Lebesgue dominated convergence theorem of the measure theory implies that the Riemann integral of a bounded sequence of continuous functions over the interval [ 0,1] pointwise converging to zero, also converges to zero. The validity of this result is independent of measure theory, on the other hand, this result together with only elementary functional analysis, can generate measure theory itself. The mentioned result was also known before the appearance of measure theory, but the original proof was very complicated. For this reason this result, when presented in teaching, is generally obtained based on measure theory. Later, Eberlein gave an elementary, but still relatively complicated proof, and there were other simpler proofs but burdened with complicated concepts, like measure theory. In this paper we give a short and elementary proof even for the following strenghened form of the mentioned result: a bounded sequence of continuous functions defined on a compact topological space K pointwise converging to zero, has a suitable convexification converging also uniformly to zero on $K,$ thus, e.g., the original sequence converges weakly to zero in C(K). This fact can also be used in the proof of the Krein-Smulian theorem. The usual proof beyond the simple tools of the functional analysis, uses heavy embedding theorems and the Riesz' representation theorem with the whole apparatus of measure theory. Our main result, however, reduces the cited proof to a form in which we need abstract tools only, namely the Hahn-Banach separation theorem and Alaoglu's theorem, without Riesz' representation or any statement of measure theory. Archive classification: math.FA The source file(s), pointwise.tex: 12973 bytes, is(are) stored in gzipped form as 0809.0393.gz with size 4kb. The corresponding postcript file has gzipped size 48kb. Submitted from: kannai(a)uni-corvinus.hu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.0393 or http://arXiv.org/abs/0809.0393 or by email in unzipped form by transmitting an empty message with subject line uget 0809.0393 or in gzipped form by using subject line get 0809.0393 to: math(a)arXiv.org.

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Abstract of a paper by Yauhen Radyna and Anna Sidorik
by alspach＠fourier.math.okstate.edu 12 Sep '08

12 Sep '08

This is an announcement for the paper "Fourier transform of function on locally compact Abelian groups taking values in Banach spaces" by Yauhen Radyna and Anna Sidorik. Abstract: We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded operator. If $G$ is an infinite group then Fourier transform $F: L_2(G,X)\to L_2(\widehat G,X)$ is a bounded operator if and only if Banach space $X$ is isomorphic to a Hilbert one. Archive classification: math.FA Mathematics Subject Classification: 46C15, 43A25 Remarks: 9 pages The source file(s), Radyna_YM_Sidorik_AG_eng.tex: 30387 bytes, is(are) stored in gzipped form as 0808.4009.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: yauhen.radyna(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.4009 or http://arXiv.org/abs/0808.4009 or by email in unzipped form by transmitting an empty message with subject line uget 0808.4009 or in gzipped form by using subject line get 0808.4009 to: math(a)arXiv.org.

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Abstract of a paper by Jeff Cheeger and Bruce Kleiner
by alspach＠fourier.math.okstate.edu 29 Aug '08

29 Aug '08

This is an announcement for the paper "Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property" by Jeff Cheeger and Bruce Kleiner. Abstract: We prove the differentiability of Lipschitz maps X---->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direction of tangent vectors to suitable rectifiable curves. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 46B22 (primary), 46G05 (secondary) The source file(s), pirnp.bbl: 3004 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.3249 or http://arXiv.org/abs/0808.3249 or by email in unzipped form by transmitting an empty message with subject line uget 0808.3249 or in gzipped form by using subject line get 0808.3249 to: math(a)arXiv.org.

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Abstract of a paper by Denis Potapov and Fyodor Sukochev
by alspach＠fourier.math.okstate.edu 29 Aug '08

29 Aug '08

This is an announcement for the paper "The Haar system in the preduals of hyperfinite factors" by Denis Potapov and Fyodor Sukochev. Abstract: We shall present examples of Schauder bases in the preduals to the hyperfinite factors of types~$\hbox{II}_1$, $\hbox{II}_\infty$, $\hbox{III}_\lambda$, $0 < \lambda \leq 1$. In the semifinite (respectively, purely infinite) setting, these systems form Schauder bases in any associated separable symmetric space of measurable operators (respectively, in any non-commutative $L^p$-space). Archive classification: math.FA Remarks: 18 pages The source file(s), haar_III_lambda.tex: 68404 bytes, is(are) stored in gzipped form as 0808.2851.gz with size 20kb. The corresponding postcript file has gzipped size 97kb. Submitted from: denis.potapov(a)flinders.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0808.2851 or http://arXiv.org/abs/0808.2851 or by email in unzipped form by transmitting an empty message with subject line uget 0808.2851 or in gzipped form by using subject line get 0808.2851 to: math(a)arXiv.org.

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