Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces

Authors

  • Jamila Jawdat Math. Dept. / Zarqa University/ Zarqa

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4800

Keywords:

Strong Coapproximation, Bochner spaces, Köthe function space

Abstract

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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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1543-1551. https://doi.org/10.29020/nybg.ejpam.v16i3.4800

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