COPROXIMINALITY RESULTS IN KÖTHE BOCHNER SPACES

Abstract

As a counterpart to best approximation in normed linear spaces, best coapproximation was introduced by Franchetti and Furi, [3], in 1972.  If X is a Banach space, E(X) the K¨othe Bochner function space and G is a closed subspace of X, the problem is: under what conditions the subspace E(G) is proximinal (coproximinal) in E(X)?  In this paper we prove that if G is a coproximinal separable subspace of X, then E(G) is coproximinal in E(X).  Some other results are presented.