TY - JOUR
AU - Jawdat, Jamila
PY - 2023/07/30
Y2 - 2023/12/07
TI - Strong Coproximinality in Bochner $L^p$-Spaces and in Köthe Spaces
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 3
SE -
DO - 10.29020/nybg.ejpam.v16i3.4800
UR - https://ejpam.com/index.php/ejpam/article/view/4800
SP - 1543-1551
AB - <p>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.</p>
ER -