Strong Coproximinality in Bochner Lp - Spaces and in Köthe Spaces.

In this paper, we study strong coproximinality in Bochner Lp -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 Lp (µ, G) is strongly coproximinal in Lp (µ, X), 1 ≤ p < ∞. 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. [ABSTRACT FROM AUTHOR]