- Banach - mathdept.okstate.edu

Abstract of a paper by Jan van Neerven
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Compactness in the Lebesgue-Bochner spaces L^p(\mu;X)" by Jan van Neerven. Abstract: Let (\Omega,\mu) be a finite measure space, X a Banach space, and let 1\le p<\infty. The aim of this paper is to give an elementary proof of the Diaz--Mayoral theorem that a subset V of L^p(\mu;X) is relatively compact if and only if it is uniformly p-integrable, uniformly tight, and scalarly relatively compact. Archive classification: math.FA Mathematics Subject Classification: Primary: 46E40, Secondary: 46E30, 46B50 Remarks: 5 pages, submitted for publication 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/1305.5688 or http://arXiv.org/abs/1305.5688

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Abstract of a paper by Diana Marcela Serrano-Rodriguez
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Absolutely \gamma-summing multilinear operators" by Diana Marcela Serrano-Rodriguez. Abstract: In this paper we introduce an abstract approach to the notion of absolutely summing multilinear operators. We show that several previous results on different contexts (absolutely summing, almost summing, Cohen summing) are particular cases of our general results. Archive classification: math.FA Submitted from: dmserrano0(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.4626 or http://arXiv.org/abs/1305.4626

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Abstract of a paper by Costas Poulios and Athanasios Tsarpalias
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Some combinatorial principles for trees and applications to tree-families in Banach spaces" by Costas Poulios and Athanasios Tsarpalias. Abstract: Suppose that $(x_s)_{s\in S}$ is a normalized family in a Banach space indexed by the dyadic tree $S$. Using Stern's combinatorial theorem we extend important results from sequences in Banach spaces to tree-families. More precisely, assuming that for any infinite chain $\beta$ of $S$ the sequence $(x_s)_{s\in\beta}$ is weakly null, we prove that there exists a subtree $T$ of $S$ such that for any infinite chain $\beta$ of $T$ the sequence $(x_s)_{s\in\beta}$ is nearly (resp., convexly) unconditional. In the case where $(f_s)_{s\in S}$ is a family of continuous functions, under some additional assumptions, we prove the existence of a subtree $T$ of $S$ such that for any infinite chain $\beta$ of $T$, the sequence $(f_s)_{s\in\beta}$ is unconditional. Finally, in the more general setting where for any chain $\beta$, $(x_s)_{s\in\beta}$ is a Schauder basic sequence, we obtain a dichotomy result concerning the semi-boundedly completeness of the sequences $(x_s)_{s\in\beta}$. Archive classification: math.FA Mathematics Subject Classification: 05D10, 46B15 Submitted from: k-poulios(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.4186 or http://arXiv.org/abs/1305.4186

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Abstract of a paper by Michael Dymond and Olga Maleva
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Differentiability inside sets with upper Minkowski dimension one" by Michael Dymond and Olga Maleva. Abstract: We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz function defined on the whole space is differentiable inside $S$. Such sets are constructed explicitly. Archive classification: math.FA Mathematics Subject Classification: 46T20 Remarks: 23 pages Submitted from: o.maleva(a)bham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.3154 or http://arXiv.org/abs/1305.3154

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Abstract of a paper by Yousef estaremi
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "multiplication conditional expectation type operators on Orlicz" by Yousef estaremi. Abstract: In this paper we consider a generalized conditional-type Holder- inequality and investigate some classic properties of multiplication conditional expectation type operators on Orlicz-spaces. Archive classification: math.FA Remarks: 12 pages Submitted from: estaremi(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.2481 or http://arXiv.org/abs/1305.2481

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Abstract of a paper by David Alonso-Gutierrez, Soeren Christensen, Markus Passenbrunner, and Joscha Prochno
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "On the Distribution of Random variables corresponding to norms" by David Alonso-Gutierrez, Soeren Christensen, Markus Passenbrunner, and Joscha Prochno. Abstract: Given a normalized Orlicz function $M$ we provide an easy formula for a distribution such that, if $X$ is a random variable distributed accordingly and $X_1,...,X_n$ are independent copies of $X$, then the expected value of the p-norm of the vector $(x_iX_i)_{i=1}^n$ is of the order $\| x \|_M$ (up to constants dependent on p only). In case $p=2$ we need the function $t\mapsto tM'(t) - M(t)$ to be $2$-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into $L_1[0,1]$. We also provide a general result replacing the $\ell_p$-norm by an arbitrary $N$-norm. This complements some deep results obtained by Gordon, Litvak, Sch\"utt, and Werner. We also prove a result in the spirit of their work which is of a simpler form and easier to apply. All results are true in the more general setting of Musielak-Orlicz spaces. Archive classification: math.FA math.PR Mathematics Subject Classification: 46B09, 46B07, 46B45, 60B99 Submitted from: joscha.prochno(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.1442 or http://arXiv.org/abs/1305.1442

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Abstract of a paper by Marek Cuth
by alspach＠math.okstate.edu 07 Jun '13

07 Jun '13

This is an announcement for the paper "Simultaneous projectional skeletons" by Marek Cuth. Abstract: We prove the existence of a simultaneous projectional skeleton for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some consequences of this result. In particular we give a new characterization of Asplund spaces using the notion of projectional skeleton. Archive classification: math.FA Mathematics Subject Classification: 46B26, 54D30 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/1305.1438 or http://arXiv.org/abs/1305.1438

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Abstract of a paper by Marius Junge and Carlos palazuelos
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "Channel capacities via $p$-summing norms" by Marius Junge and Carlos palazuelos. Abstract: In this paper we show how \emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \emph{Shannon's information theory}. Furthermore, in the last years Shannon's theory has been generalized to the quantum setting to let the \emph{quantum information theory} step in. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. In particular these capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. To deal with the quantum case we will use the noncommutative version of $p$-summing maps. More precisely, we prove that the (product state) classical capacity of a quantum channel with restricted assisted entanglement can be expressed as the derivative of a completely $p$-summing norm. Archive classification: math.FA math.OA quant-ph Submitted from: carlospalazuelos(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.1020 or http://arXiv.org/abs/1305.1020

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Abstract of a paper by L.K.Vashisht and Geetika Khattar
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "On $\mathfrak{I}$-reconstruction property" by L.K.Vashisht and Geetika Khattar. Abstract: Reconstruction property in Banach spaces introduced and studied by Casazza and Christensen in [1]. In this paper we introduce reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property. A characterization of reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property in terms of frames in Banach spaces is obtained. Banach frames associated with reconstruction property are discussed. Archive classification: math.FA Mathematics Subject Classification: 42C15, 42C30, 46B15 Submitted from: lalitkvashisht(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.0334 or http://arXiv.org/abs/1305.0334

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Abstract of a paper by Krzysztof Bolibok, Andrzej Wisnicki and Jacek Wosko
by alspach＠math.okstate.edu 07 May '13

07 May '13

This is an announcement for the paper "The minimal displacement and extremal spaces" by Krzysztof Bolibok, Andrzej Wisnicki and Jacek Wosko. Abstract: We show that both separable preduals of $L_{1}$ and non-type I $C^*$-algebras are strictly extremal with respect to the minimal displacement of $k$-Lipschitz mappings acting on the unit ball of a Banach space. In particular, every separable $C(K)$ space is strictly extremal. Archive classification: math.FA Submitted from: awisnic(a)hektor.umcs.lublin.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1305.0246 or http://arXiv.org/abs/1305.0246

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