September 2013 - Banach - mathdept.okstate.edu

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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