%0 Journal Article
%A Mendoza Casas, José
%A Pakhrou, Tijani
%T Best simultaneous approximation in L-1 (mu, X)
%D 2007
%@ 0021-9045
%U https://hdl.handle.net/20.500.14352/50160
%X Let X be a Banach space, (Omega, Sigma, mu) a finite measure space, and L-1 (mu, X) the Banach space of X-valued Bochner mu-integrable functions defined on Omega endowed with its usual norm. Let us suppose that Sigma(0) is a sub-sigma-algebra of Sigma, and let mu(0) be the restriction of mu to Sigma(0). Given a natural number n, let N be a monotonous norm in R-n. It is shown that if X is reflexive then L-1 (mu(0), X) is N-simultaneously proximinal in L-1 (mu, X) in the sense of Fathi et al. [Best simultaneous approximation in L-p(I, E), J. Approx. Theory 116 (2002), 369-379]. Some examples and remarks related with N-simultaneous proximinality are also given.
%~