April 2008 - Banach - mathdept.okstate.edu

Abstract of a paper by Michael Doree, Olga Maleva
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "A compact null set containing a differentiability point of every Lipschitz function" by Michael Doree and Olga Maleva. Abstract: We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly. Archive classification: math.FA math.CA Mathematics Subject Classification: 46G05; 46T20 Remarks: 31 pages The source file(s), DoreMaleva.tex: 76535 bytes, is(are) stored in gzipped form as 0804.4576.gz with size 22kb. The corresponding postcript file has gzipped size 144kb. Submitted from: o.maleva(a)warwick.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.4576 or http://arXiv.org/abs/0804.4576 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4576 or in gzipped form by using subject line get 0804.4576 to: math(a)arXiv.org.

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Abstract of a paper by Jarno Talponen
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "The isometry group of L^{p}(\mu,\X) is SOT-contractible" by Jarno Talponen. Abstract: We will show that if (\Omega,\Sigma,\mu) is an atomless positive measure space, X is a Banach space and 1\leq p<\infty, then the group of isometric automorphisms on the Bochner space L^{p}(\mu,X) is contractible in the strong operator topology. We do not require \Sigma or X above to be separable. Archive classification: math.FA Mathematics Subject Classification: 46B04; 46B25; 46E40 The source file(s), contr32.tex: 27449 bytes, is(are) stored in gzipped form as 0804.4427.gz with size 9kb. The corresponding postcript file has gzipped size 75kb. 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/0804.4427 or http://arXiv.org/abs/0804.4427 or by email in unzipped form by transmitting an empty message with subject line uget 0804.4427 or in gzipped form by using subject line get 0804.4427 to: math(a)arXiv.org.

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Abstract of a paper by Andrea Colesanti and Eugenia Saorin-Gomez
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals" by Andrea Colesanti and Eugenia Saorin-Gomez. Abstract: We use Brunn-Minkowski inequalities for quermassintegrals to deduce a family of inequalities of Poincar\'e type on the unit sphere and on the boundary of smooth convex bodies in the $n$-dimensional Euclidean space. Archive classification: math.FA math.MG Mathematics Subject Classification: 52A20; 26D10 Remarks: 15 pages The source file(s), cs3.tex: 37802 bytes, is(are) stored in gzipped form as 0804.3867.gz with size 12kb. The corresponding postcript file has gzipped size 109kb. Submitted from: colesant(a)math.unifi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3867 or http://arXiv.org/abs/0804.3867 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3867 or in gzipped form by using subject line get 0804.3867 to: math(a)arXiv.org.

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Abstract of a paper by Matthew Daws, Hung Le Pham and Stuart White
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" by Matthew Daws, Hung Le Pham and Stuart White. Abstract: We investigate possible preduals of the measure algebra $M(G)$ of a locally compact group and the Fourier algebra $A(G)$ of a separable compact group. Both of these algebras are canonically dual spaces and the canonical preduals make the multiplication separately weak$^*$-continuous so that these algebras are dual Banach algebras. In this paper we find additional conditions under which the preduals $C_0(G)$ of $M(G)$ and $C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a natural coassociative multiplication and show that the canonical predual gives rise to the unique weak$^*$-topology making both the multiplication separately weak$^*$-continuous and the coassociative multiplication weak$^*$-continuous. In particular, dual cohomological properties of these algebras are well defined with this additional structure. Archive classification: math.FA math.OA Mathematics Subject Classification: 43A20, 43A77 Remarks: 21 pages The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are) stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding postcript file has gzipped size 133kb. Submitted from: matt.daws(a)cantab.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3764 or http://arXiv.org/abs/0804.3764 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3764 or in gzipped form by using subject line get 0804.3764 to: math(a)arXiv.org.

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Abstract of a paper by Venta Terauds
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "Functional calculus extensions on dual spaces" by Venta Terauds. Abstract: In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one. Archive classification: math.FA Mathematics Subject Classification: 47B40 Remarks: 7 pages The source file(s), func_calc_extns_terauds.tex: 24129 bytes, is(are) stored in gzipped form as 0804.3451.gz with size 7kb. The corresponding postcript file has gzipped size 70kb. Submitted from: venta.terauds(a)newcastle.edu.au The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3451 or http://arXiv.org/abs/0804.3451 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3451 or in gzipped form by using subject line get 0804.3451 to: math(a)arXiv.org.

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Abstract of a paper by Mark Veraar and Tuomas Hytonen
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "R-boundedness of smooth operator-valued functions" by Mark Veraar and Tuomas Hytonen. Abstract: In this paper we study $R$-boundedness of operator families $\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach spaces. Under cotype and type assumptions on $X$ and $Y$ we give sufficient conditions for $R$-boundedness. In the first part we show that certain integral operator are $R$-bounded. This will be used to obtain $R$-boundedness in the case that $\mathcal{T}$ is the range of an operator-valued function $T:\R^d\to \calL(X,Y)$ which is in a certain Besov space $B^{d/r}_{r,1}(\R^d;\calL(X,Y))$. The results will be applied to obtain $R$-boundedness of semigroups and evolution families, and to obtain sufficient conditions for existence of solutions for stochastic Cauchy problems. Archive classification: math.FA math.PR Mathematics Subject Classification: 47B99; 46B09; 46E35; 46E40 The source file(s), rboundedsmooth_arxiv.tex: 81153 bytes, is(are) stored in gzipped form as 0804.3313.gz with size 24kb. The corresponding postcript file has gzipped size 142kb. Submitted from: mark(a)profsonline.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3313 or http://arXiv.org/abs/0804.3313 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3313 or in gzipped form by using subject line get 0804.3313 to: math(a)arXiv.org.

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Abstract of a paper by Dusan Repovs and Pavel V. Semenov
by alspach＠fourier.math.okstate.edu 30 Apr '08

30 Apr '08

This is an announcement for the paper "A unified construction yielding precisely Hilbert and James sequences spaces" by Dusan Repovs and Pavel V. Semenov. Abstract: Following James' approach, we shall define the Banach space $J(e)$ for each vector $e=(e_1,e_2,...,e_d) \in \Bbb{R}^d$ with $ e_1 \ne 0$. The construction immediately implies that $J(1)$ coincides with the Hilbert space $i_2$ and that $J(1;-1)$ coincides with the celebrated quasireflexive James space $J$. The results of this paper show that, up to an isomorphism, there are only the following two possibilities: (i) either $J(e)$ is isomorphic to $l_2$ ,if $e_1+e_2+...+e_d\ne 0$ (ii) or $J(e)$ is isomorphic to $J$. Such a dichotomy also holds for every separable Orlicz sequence space $l_M$. Archive classification: math.GN math.FA Mathematics Subject Classification: 54C60; 54C65; 41A65; 54C55; 54C20 The source file(s), ArchiveVersion.tex: 21648 bytes, is(are) stored in gzipped form as 0804.3131.gz with size 8kb. The corresponding postcript file has gzipped size 65kb. Submitted from: dusan.repovs(a)guest.arnes.si The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3131 or http://arXiv.org/abs/0804.3131 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3131 or in gzipped form by using subject line get 0804.3131 to: math(a)arXiv.org.

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Abstract of a paper by Hirbod Assa
by alspach＠fourier.math.okstate.edu 18 Apr '08

18 Apr '08

This is an announcement for the paper "Characterization of compact subsets of $\mathcal{A}^p$ with respect to weak topology" by Hirbod Assa. Abstract: In this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak topology induced by $\mathcal{A}^p$, was recently employed to create the convex risk theory of random processes. The weak compact sets of $\mathcal{A}^p$ are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on $\mathcal{R}^q$ and for their use in the optimization theory. Archive classification: math.PR math.FA Remarks: 8 pages The source file(s), compactsetsAssa.H.tex: 19008 bytes, is(are) stored in gzipped form as 0804.2873.gz with size 6kb. The corresponding postcript file has gzipped size 67kb. Submitted from: assa(a)dms.umontreal.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2873 or http://arXiv.org/abs/0804.2873 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2873 or in gzipped form by using subject line get 0804.2873 to: math(a)arXiv.org.

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Abstract of a paper by Boris Burshteyn
by alspach＠fourier.math.okstate.edu 18 Apr '08

18 Apr '08

This is an announcement for the paper "Uniform lamda-adjustment and mu-approximation in Banach spaces" by Boris Burshteyn. Abstract: We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform lambda-adjustment which is weaker than perturbations by small gap, operator norm, q-norm, and K2-approximation. In arbitrary Banach spaces some of the classical Fredholm stability theorems remain true under uniform lambda-adjustment, while other fail. However, uniformly lambda-adjusted subspaces and linear operators retain their (semi--)Fredholm properties in a Banach space which dual is Fr\'{e}chet-Urysohn in weak* topology. We also introduce another concept of perturbation called uniform mu-approximation which is weaker than perturbations by small gap, norm, and compact convergence, yet stronger than uniform lambda-adjustment. We present Fredholm stability theorems for uniform mu-approximation in arbitrary Banach spaces and a theorem on stability of Riesz kernels and ranges for commuting closed essentially Kato operators. Finally, we define the new concepts of a tuple of subspaces and of a complex of subspaces in Banach spaces, and present stability theorems for index and defect numbers of Fredholm tuples and complexes under uniform lambda-adjustment and uniform mu-approximation. Archive classification: math.FA Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55; 47B07; Remarks: 90 pages The source file(s), boris997paper1.tex: 300886 bytes (looks big), is(are) stored in gzipped form as 0804.2832.gz with size 63kb. The corresponding postcript file has gzipped size 446kb. Submitted from: boris997(a)astound.net The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2832 or http://arXiv.org/abs/0804.2832 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2832 or in gzipped form by using subject line get 0804.2832 to: math(a)arXiv.org.

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Abstract of a paper by Ostrovsky E. Sirota L
by alspach＠fourier.math.okstate.edu 18 Apr '08

18 Apr '08

This is an announcement for the paper "Nikol'skii-type inequalities for rearrangement invariant spaces" by Ostrovsky E. Sirota L. Abstract: In this paper we generalize the classical Nikol'skii inequality on the many popular classes pairs of rearrangement invariant (r.i.) spaces and construct some examples in order to show the exactness of our estimations. Archive classification: math.FA Mathematics Subject Classification: 60G17 The source file(s), Nik14_4.tex: 40903 bytes, is(are) stored in gzipped form as 0804.2311.gz with size 14kb. The corresponding postcript file has gzipped size 85kb. Submitted from: leos(a)post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.2311 or http://arXiv.org/abs/0804.2311 or by email in unzipped form by transmitting an empty message with subject line uget 0804.2311 or in gzipped form by using subject line get 0804.2311 to: math(a)arXiv.org.

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