Mendoza Casas, José2023-06-202023-06-201998-05-020021-904510.1006/jath.1997.3163https://hdl.handle.net/20.500.14352/57653Let 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0021904597931634http://www.sciencedirect.com/restricted access517.98proximinal subspacesbest approximation in Lp (μX).Análisis funcional y teoría de operadores