%0 Journal Article
%A Mendoza Casas, José
%T Proximinality in L-p(mu,X).
%D 1998
%@ 0021-9045
%U https://hdl.handle.net/20.500.14352/57653
%X Let X be a Banach space and let Y be a closed subspace of X. Let 1 less than or equal to p less than or equal to infinity and let us denote by L-p(mu, X) the Banach space of all X-valued Bochner p-integrable (essentially bounded for p = infinity) functions on a certain positive complete sigma-finite measure space (Omega, Sigma, mu), endowed with the usual p-norm. In this paper we give a negative answer to the following question: "If Y is proximinal in X, is L-p(mu, Y) proximinal in L-p(mu, X)?" We also show that the answer is affirmative for separable spaces Y. Some consequences of this are obtained.
%~