Bochner $L^p$-空间和Köthe空间中的强共邻性

IF 1 Q1 MATHEMATICS
J. Jawdat
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引用次数: 0

摘要

本文研究了Bochner $L^p$ -空间和Köthe Bochner函数空间$E(X)$中的强近性。我们研究了在Banach空间$X$的子空间$G$上,使$L^{p}\left(\mu,G \right)$在$L^{p}\left(\mu,X \right), 1 \leq p <\infty$上是强近邻的一些条件。另一方面,我们证明了如果$G$是$X$的可分子空间,则当且仅当$E(G)$是$E(X)$的强近邻空间,且$E$是严格单调的Köthe空间,则$G$是$X$的强近邻空间。这概括了文献中的一些结果。本文还介绍了这方面的一些其他结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces
In this paper, we study strong coproximinality in Bochner $L^p$-spaces and in the Köthe Bochner function space $E(X)$. We investigate some conditions to be imposed on the subspace $G$ of the Banach space $X$ such that $L^{p}\left(\mu,G \right)$ is strongly coproximinal in $L^{p}\left(\mu,X \right), 1 \leq p <\infty$. On the other hand, we prove that if $G$ is a separable subspace of $X$ then $G$ is strongly coproximinal in $X$ if and only if $E(G)$ is strongly coproximinal in $E(X)$, provided that $E$ is a strictly monotone Köthe space. This generalizes some results in the literature. Some other results in this direction are also presented.
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来源期刊
CiteScore
1.30
自引率
28.60%
发文量
156
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