Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Piotr Niemiec
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "Bounded convergence theorems" by Piotr Niemiec. Abstract: There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X,E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X,E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved. Archive classification: math.FA Mathematics Subject Classification: Primary 46G10, Secondary 46E40 Remarks: 31 pages Submitted from: piotr.niemiec(a)uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.2612 or http://arXiv.org/abs/1309.2612

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Abstract of a paper by Marek Cuth, Martin Rmoutil, and Miroslav Zeleny
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "On separable determination of sigma-P-porous sets in Banach spaces" by Marek Cuth, Martin Rmoutil, and Miroslav Zeleny. Abstract: We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be from a rather wide class of porosity-like relations in complete metric spaces. In particular, we separably reduce the notion of Suslin cone small set in Asplund spaces. As an application we prove a theorem stating that a continuous approximately convex function on an Asplund space is Frechet differentiable up to a cone small set. Archive classification: math.FA Mathematics Subject Classification: 46B26, 28A05, 54E35, 58C20 Submitted from: cuthm5am(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.2174 or http://arXiv.org/abs/1309.2174

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Abstract of a paper by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "Almost limited sets in Banach lattices" by Jin Xi Chen, Zi Li Chen, and Guo Xing Ji. Abstract: We introduce and study the class of almost limited sets in Banach lattices, that is, sets on which every disjoint weak$^{*}$ null sequence of functionals converges uniformly to zero. It is established that a Banach lattice has order continuous norm if and only if almost limited sets and $L$-weakly compact sets coincide. In particular, in terms of almost Dunford-Pettis operators into $c_{0}$, we give an operator characterization of those $\sigma$-Dedekind complete Banach lattices whose relatively weakly compact sets are almost limited, that is, for a $\sigma$-Dedekind Banach lattice $E$, every relatively weakly compact set in $E$ is almost limited if and only if every continuous linear operator $T:E\rightarrow c_{0}$ is an almost Dunford-Pettis operator. Archive classification: math.FA Mathematics Subject Classification: Primary 46B42, Secondary 46B50, 47B65 Remarks: 11 pages Submitted from: jinxichen(a)home.swjtu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.2020 or http://arXiv.org/abs/1309.2020

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Abstract of a paper by Joaquim Martin and Mario Milman
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "Integral isoperimetric transference and dimensionless Sobolev inequalities" by Joaquim Martin and Mario Milman. Abstract: We introduce the concept of Gaussian integral isoperimetric transference and show how it can be applied to obtain a new class of sharp Sobolev-Poincar\'{e} inequalities with constants independent of the dimension. In the special case of $L^{q}$ spaces on the unit $n-$dimensional cube our results extend the recent inequalities that were obtained in \cite{FKS} using extrapolation. Archive classification: math.FA Submitted from: mario.milman(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.1980 or http://arXiv.org/abs/1309.1980

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Abstract of a paper by Krzysztof Chris Ciesielski, Jose L. Gamez-Merino, Daniel Pellegrino, and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "Lineability, spaceability, and additivity cardinals for Darboux-like functions" by Krzysztof Chris Ciesielski, Jose L. Gamez-Merino, Daniel Pellegrino, and Juan B. Seoane-Sepulveda. Abstract: We introduce the concept of {\em maximal lineability cardinal number}, $\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\HL(M)$, and lineability $\LL(M)$ of $M$. In particular, we will describe, in terms of $\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\real^n$, $n\ge 1$: extendable, Jones, and almost continuous functions. Archive classification: math.FA Submitted from: jseoane(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.1965 or http://arXiv.org/abs/1309.1965

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Abstract of a paper by Witold Marciszewski and Grzegorz Plebanek
by alspach＠math.okstate.edu 23 Sep '13

23 Sep '13

This is an announcement for the paper "On Borel structures in the Banach space C(\beta\omega)" by Witold Marciszewski and Grzegorz Plebanek. Abstract: M. Talagrand showed that, for the Cech-Stone compactification \beta\omega\ of the space of natural numbers, the norm and the weak topology generate different Borel structures in the Banach space C(\beta\omega). We prove that the Borel structures in C(\beta\omega) generated by the weak and the pointwise topology are also different. We also show that in C(\omega*), where \omega*=\beta\omega - \omega, there is no countable family of pointwise Borel sets separating functions from C(\omega*). Archive classification: math.FA Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05 Remarks: 14 pages Submitted from: grzes(a)math.uni.wroc.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.1908 or http://arXiv.org/abs/1309.1908

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Abstract of a paper by Leandro Candido
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "On embeddings of $C_0(K)$ spaces into $C_0(J,X)$ spaces" by Leandro Candido. Abstract: Let $C_0(K, X)$ denote the space of all continuous $X$-valued functions defined on the locally compact Hausdorff space $K$ which vanish at infinity, provided with the supremum norm. If $X$ is the scalar field, we denote $C_0(K, X)$ by simply $C_0(K)$. If $K$ is compact these spaces will be denoted by $C(K,X)$ and $C(K)$ respectively. In this paper we study whether some aspects of the space $K$ are determined by $J$ and the geometry of the Banach space $X$, if there is a linear embeddind of $C_0(K)$ into $C_0(J,X)$. Archive classification: math.FA Mathematics Subject Classification: Primary 46E40, Secondary 46B25 Submitted from: lc(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6555 or http://arXiv.org/abs/1308.6555

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Abstract of a paper by Michael Dymond
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Avoiding sigma-porous sets in Hilbert spaces" by Michael Dymond. Abstract: We give a constructive proof that any $\sigma$-porous subset of a Hilbert space has Lebesgue measure zero on typical $C^{1}$ curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-$p$ porous sets may meet many $C^{1}$ curves in positive measure. Archive classification: math.FA Submitted from: dymondm(a)maths.bham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6420 or http://arXiv.org/abs/1308.6420

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Abstract of a paper by Hui Zhang and Lizhi Cheng
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "New bounds for circulant Johnson-Lindenstrauss embeddings" by Hui Zhang and Lizhi Cheng. Abstract: This paper analyzes circulant Johnson-Lindenstrauss (JL) embeddings which, as an important class of structured random JL embeddings, are formed by randomizing the column signs of a circulant matrix generated by a random vector. With the help of recent decoupling techniques and matrix-valued Bernstein inequalities, we obtain a new bound $k=O(\epsilon^{-2}\log^{(1+\delta)} (n))$ for Gaussian circulant JL embeddings. Moreover, by using the Laplace transform technique (also called Bernstein's trick), we extend the result to subgaussian case. The bounds in this paper offer a small improvement over the current best bounds for Gaussian circulant JL embeddings for certain parameter regimes and are derived using more direct methods. Archive classification: cs.IT math.FA math.IT Remarks: 11 pages; accepted by Communications in Mathematical Sciences Submitted from: h.zhang1984(a)163.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6339 or http://arXiv.org/abs/1308.6339

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Abstract of a paper by Fernando Albiac and Jose L Ansorena
by alspach＠math.okstate.edu 30 Aug '13

30 Aug '13

This is an announcement for the paper "Optimal average approximations for functions mapping in quasi-Banach spaces" by Fernando Albiac and Jose L Ansorena. Abstract: In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1, and the question arose whether such a significant result might hold in some non-Banach spaces. In this article we completely settle the problem by proving that the fundamental theorem of calculus breaks down in the context of any non-locally convex quasi-Banach space. Our approach introduces the tool of Riemann-integral averages of continuous functions, and uses it to bring out to light the differences in behavior of their approximates in the lack of local convexity. As a by-product of our work we solve a problem raised in [F. Albiac and J.L. Ansorena, Lipschitz maps and primitives for continuous functions in quasi-Banach space, Nonlinear Anal. 75 (2012), no. 16, 6108-6119] on the different types of spaces of differentiable functions with values on a quasi-Banach space. Archive classification: math.FA Mathematics Subject Classification: 46A16, 46G05 Remarks: 14 pages Submitted from: joseluis.ansorena(a)unirioja.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1308.6127 or http://arXiv.org/abs/1308.6127

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