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

按检索

Conditional weak compactness in vector-valued function spaces

Authors:	Marian Nowak

Institution:	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 $\sigma$ -finite measure space $(\Omega ,\Sigma ,\mu )$ and let $E^{\prime }$ be the Köthe dual of with $\hbox {supp}\,E^{\prime }=\Omega$ . Let $(X,\Vert\cdot \Vert _{X})$ 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 $f\colon \, \Omega \to X$ and consisting of all those $f\in L^{0}(X)$ for which the scalar function $\Vert f(\cdot )\Vert _{X}$ belongs to . For a subset of for which the set $\{\Vert f(\cdot )\Vert _{X}\colon \, f\in H\}$ is $\sigma (E,E^{\prime })$ -bounded the following statement is equivalent to conditional $\sigma (E(X),E^{\prime }(X^{}))$ -compactness: the set $\{\Vert f(\cdot )\Vert _{X}\colon \, f\in H\}$ is conditionally $\sigma (E,E^{\prime })$ -compact and $\{\int _{A} f(\omega )d\mu \colon \, f\in H\}$ is a conditionally weakly compact subset of for each $A\in \Sigma$ , $\mu(A)<\infty$ 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》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏