Banach June 2009

banach@mathdept.okstate.edu

2 participants
19 discussions

Abstract of a paper by Jan van Neerven and Lutz Weis
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Vector measures of bounded gamma-variation and stochastic integrals" by Jan van Neerven and Lutz Weis. Abstract: We introduce the class of vector measures of bounded $\gamma$-variation and study its relationship with vector-valued stochastic integrals with respect to Brownian motions. Archive classification: math.FA math.PR Mathematics Subject Classification: 46G10, 60H05 Remarks: 9 pages; to appear in the proceedings of 3rd Meeting on Vector Measures, Integration and Applications (Eichstaett, 2008) The source file(s), VanNeervenWeis.pdf: 136678 bytes VanNeervenWeis_final_version.tex: 24984 bytes birkmult.cls: 60110 bytes newsymbol.sty: 440 bytes srcltx.sty: 6955 bytes, is(are) stored in gzipped form as 0906.1883.tar.gz with size 141kb. The corresponding postcript file has gzipped size 76kb. Submitted from: J.M.A.M.vanNeerven(a)tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.1883 or http://arXiv.org/abs/0906.1883 or by email in unzipped form by transmitting an empty message with subject line uget 0906.1883 or in gzipped form by using subject line get 0906.1883 to: math(a)arXiv.org.

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Abstract of a paper by Luis Dubarbie
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Separating maps between spaces of vector-valued absolutely continuous functions" by Luis Dubarbie. Abstract: In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied. Archive classification: math.FA Mathematics Subject Classification: 47B38; 46E15, 46E40, 46H40, 47B33 Remarks: Canadian Mathematical Bulletin, to appear The source file(s), cmb-9158.tex: 30683 bytes, is(are) stored in gzipped form as 0906.1633.gz with size 9kb. The corresponding postcript file has gzipped size 73kb. Submitted from: luis.dubarbie(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.1633 or http://arXiv.org/abs/0906.1633 or by email in unzipped form by transmitting an empty message with subject line uget 0906.1633 or in gzipped form by using subject line get 0906.1633 to: math(a)arXiv.org.

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Abstract of a paper by E. Odell, B. Sari, Th. Schlumprecht, and B. Zheng
by alspach＠fourier.math.okstate.edu 29 Jun '09

29 Jun '09

This is an announcement for the paper "Systems formed by translates of one element in $L_p(\mathbb R)$" by E. Odell, B. Sari, Th. Schlumprecht, and B. Zheng. Abstract: Let $1\le p <\infty$, $f\in L_p(\real)$ and $\Lambda\subseteq \real$. We consider the closed subspace of $L_p(\real)$, $X_p (f,\Lambda)$, generated by the set of translations $f_{(\lambda)}$ of $f$ by $\lambda \in\Lambda$. If $p=1$ and $\{f_{(\lambda)} :\lambda\in\Lambda\}$ is a bounded minimal system in $L_1(\real)$, we prove that $X_1 (f,\Lambda)$ embeds almost isometrically into $\ell_1$. If $\{f_{(\lambda)} :\lambda\in\Lambda\}$ is an unconditional basic sequence in $L_p(\real)$, then $\{f_{(\lambda)} : \lambda\in\Lambda\}$ is equivalent to the unit vector basis of $\ell_p$ for $1\le p\le 2$ and $X_p (f,\Lambda)$ embeds into $\ell_p$ if $2<p\le 4$. If $p>4$, there exists $f\in L_p(\real)$ and $\Lambda \subseteq \zed$ so that $\{f_{(\lambda)} :\lambda\in\Lambda\}$ is unconditional basic and $L_p(\real)$ embeds isomorphically into $X_p (f,\Lambda)$. Archive classification: math.FA The source file(s), ossz.tex: 98122 bytes, is(are) stored in gzipped form as 0906.1162.gz with size 28kb. The corresponding postcript file has gzipped size 157kb. Submitted from: bunyamin(a)unt.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.1162 or http://arXiv.org/abs/0906.1162 or by email in unzipped form by transmitting an empty message with subject line uget 0906.1162 or in gzipped form by using subject line get 0906.1162 to: math(a)arXiv.org.

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Abstract of a paper by Denny H. Leung
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "Biseparating maps on generalized Lipschitz spaces" by Denny H. Leung. Abstract: Let $X, Y$ be complete metric spaces and $E, F$ be Banach spaces. If $A(X,E)$ and $A(Y,F)$ stand for certain spaces of functions from $X$ to $E$ and from $Y$ to $F$ respectively, a bijective linear operator $T: A(X,E) \to A(Y,F)$ is said to be biseparating if $f$ and $g \in A(X,E)$ are disjoint if and only if $Tf$ and $Tg$ are disjoint. When $A(X,E)$ and $A(Y,F)$ are either the space of Lipschitz functions of order $\alpha$, the space of little Lipschitz functions of order $\alpha$, or the space of uniformly continuous functions, every linear biseparating map between them is characterized as a weighted composition operator, i.e., of the form $Tf(y) = S_y(f(h^{-1}(y))$ for a family of vector space isomorphisms $S_y: E \to F$ and a homeomorphism $h : X\to Y$. We also investigate the continuity of $T$ and the possibility of having biseparating maps between different classes of spaces. Here the functions involved (as well as the metric spaces $X$ and $Y$) may be unbounded. Also, the arguments do not require the use of compactification of the spaces $X$ and $Y$. Archive classification: math.FA Mathematics Subject Classification: 47B38 The source file(s), Lipschitz3.tex: 62347 bytes, is(are) stored in gzipped form as 0906.0221.gz with size 18kb. The corresponding postcript file has gzipped size 118kb. Submitted from: matlhh(a)nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.0221 or http://arXiv.org/abs/0906.0221 or by email in unzipped form by transmitting an empty message with subject line uget 0906.0221 or in gzipped form by using subject line get 0906.0221 to: math(a)arXiv.org.

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Abstract of a paper by Denny H. Leung and Wee-Kee Tang
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "Banach-Stone Theorems for maps preserving common zeros" by Denny H. Leung and Wee-Kee Tang. Abstract: Let $X$ and $Y$ be completely regular spaces and $E$ and $F$ be Hausdorff topological vector spaces. We call a linear map $T$ from a subspace of $C(X,E)$ into $C(Y,F)$ a \emph{Banach-Stone map} if it has the form $Tf(y) = S_{y}(f(h(y))$ for a family of linear operators $S_{y} : E \to F$, $y \in Y$, and a function $h: Y \to X$. In this paper, we consider maps having the property: \cap^{k}_{i=1}Z(f_{i}) \neq\emptyset\iff\cap^{k}_{i=1}Z(Tf_{i}) \neq \emptyset, where $Z(f) = \{f = 0\}$. We characterize linear bijections with property (Z) between spaces of continuous functions, respectively, spaces of differentiable functions (including $C^{\infty}$), as Banach-Stone maps. In particular, we confirm a conjecture of Ercan and \"{O}nal: Suppose that $X$ and $Y$ are realcompact spaces and $E$ and $F$ are Hausdorff topological vector lattices (respectively, $C^{*}$-algebras). Let $T: C(X,E) \to C(Y,F)$ be a vector lattice isomorphism (respectively, $*$-algebra isomorphism) such that Z(f) \neq\emptyset\iff Z(Tf) \neq\emptyset. Then $X$ is homeomorphic to $Y$ and $E$ is lattice isomorphic (respectively, $C^{*}$-isomorphic) to $F$. Some results concerning the continuity of $T$ are also obtained. Archive classification: math.FA Mathematics Subject Classification: 47B38 The source file(s), Banach_Stone_Lattice6.tex: 92258 bytes, is(are) stored in gzipped form as 0906.0219.gz with size 21kb. The corresponding postcript file has gzipped size 140kb. Submitted from: matlhh(a)nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.0219 or http://arXiv.org/abs/0906.0219 or by email in unzipped form by transmitting an empty message with subject line uget 0906.0219 or in gzipped form by using subject line get 0906.0219 to: math(a)arXiv.org.

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Abstract of a paper by Petr Hajek and Richard J. Smith
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "Operator machines on directed graphs" by Petr Hajek and Richard J. Smith. Abstract: We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if x in X\A then some subsequence of (R^n(x)) converges weakly to x. This answers in the negative a recent conjecture of Prajitura. The result can be extended to any Banach space containing an infinite-dimensional, complemented subspace with a symmetric basis; in particular, all 'classical' Banach spaces admit such an operator. Archive classification: math.FA Mathematics Subject Classification: 47A05 The source file(s), machines14.tex: 47356 bytes, is(are) stored in gzipped form as 0906.0160.gz with size 14kb. The corresponding postcript file has gzipped size 111kb. 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/0906.0160 or http://arXiv.org/abs/0906.0160 or by email in unzipped form by transmitting an empty message with subject line uget 0906.0160 or in gzipped form by using subject line get 0906.0160 to: math(a)arXiv.org.

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Abstract of a paper by P. L. Combettes and N. N. Reyes
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "Functions with prescribed best linear approximations" by P. L. Combettes and N. N. Reyes. Abstract: A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions to such problems. A finite family of subspaces is said to satisfy the \emph{Inverse Best Approximation Property (IBAP)} if there exists a point that admits any selection of points from these subspaces as best approximations. We provide various characterizations of the IBAP in terms of the geometry of the subspaces. Connections between the IBAP and the linear convergence rate of the periodic projection algorithm for solving the underlying affine feasibility problem are also established. The results are applied to problems in harmonic analysis, integral equations, signal theory, and wavelet frames. Archive classification: math.FA Mathematics Subject Classification: 41A50, 41A65, 65T60 The source file(s), arxiv1.tex: 79105 bytes, is(are) stored in gzipped form as 0905.3520.gz with size 21kb. The corresponding postcript file has gzipped size 162kb. Submitted from: plc(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0905.3520 or http://arXiv.org/abs/0905.3520 or by email in unzipped form by transmitting an empty message with subject line uget 0905.3520 or in gzipped form by using subject line get 0905.3520 to: math(a)arXiv.org.

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Abstract of a paper by S.J. Dilworth, E. Odell, Th. Schlumprecht, and A. Zsak
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "On the convergence of greedy algorithms for initial segments of the Haar basis" by S.J. Dilworth, E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: We consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in $L_p[0,1]$ ($1 < p < \infty$) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases. Archive classification: math.FA Mathematics Subject Classification: 41A65 ;42A10 The source file(s), dosz_greedy.tex: 33654 bytes, is(are) stored in gzipped form as 0905.3036.gz with size 11kb. The corresponding postcript file has gzipped size 102kb. 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/0905.3036 or http://arXiv.org/abs/0905.3036 or by email in unzipped form by transmitting an empty message with subject line uget 0905.3036 or in gzipped form by using subject line get 0905.3036 to: math(a)arXiv.org.

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Abstract of a paper by G. Botelho, D. Diniz, D. Pellegrino and E. Teixeira
by alspach＠fourier.math.okstate.edu 05 Jun '09

05 Jun '09

This is an announcement for the paper "A note on lineability" by G. Botelho, D. Diniz, D. Pellegrino and E. Teixeira. Abstract: In this note we answer a question concerning lineability of the set of non-absolutely summing operators. Archive classification: math.FA Mathematics Subject Classification: 47B10, 47B37, Remarks: 4 pages The source file(s), note-lineability13Maio2009.tex: 11166 bytes, is(are) stored in gzipped form as 0905.2677.gz with size 4kb. The corresponding postcript file has gzipped size 50kb. Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0905.2677 or http://arXiv.org/abs/0905.2677 or by email in unzipped form by transmitting an empty message with subject line uget 0905.2677 or in gzipped form by using subject line get 0905.2677 to: math(a)arXiv.org.

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Banach June 2009