RT Journal Article
T1 Proximinality in L-p(mu,X).
A1 Mendoza Casas, José
AB 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.
PB Academic Press-Elsevier Science
SN 0021-9045
YR 1998
FD 1998-05-02
LK https://hdl.handle.net/20.500.14352/57653
UL https://hdl.handle.net/20.500.14352/57653
LA eng
NO D.G.I.C.Y.T.
DS Docta Complutense
RD 4 abr 2025