Conditional weak compactness in vector-valued function spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Conditional weak compactness in vector-valued function spaces

Authors:	Marian Nowak

Affiliation:	Institute of Mathematics, T. Kotarbinski Pedagogical University, Pl. Slowianski 9, 65--069 Zielona Góra, Poland

Abstract:	Let be an ideal of $L^{0}$ over a -finite measure space and let $E^{prime }$ be the Köthe dual of with $hbox {supp},E^{prime }=Omega$ . Let $(X,Vertcdot Vert _{X})$ be a real Banach space, and $X^{}$ the topological dual of . Let be a subspace of the space $L^{0}(X)$ of equivalence classes of strongly measurable functions and consisting of all those $fin L^{0}(X)$ for which the scalar function $Vert f(cdot )Vert _{X}$ belongs to . For a subset of for which the set ${Vert f(cdot )Vert _{X}colon , fin H}$ is $sigma (E,E^{prime })$ -bounded the following statement is equivalent to conditional $sigma (E(X),E^{prime }(X^{}))$ -compactness: the set ${Vert f(cdot )Vert _{X}colon , fin H}$ is conditionally $sigma (E,E^{prime })$ -compact and ${int _{A} f(omega )dmu colon , fin H}$ is a conditionally weakly compact subset of for each , with $chi _{A}in E^{prime }$ . Applications to Orlicz-Bochner spaces are given.

Keywords:	Conditional weak compactness vector valued function spaces

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文