Resumen de Best simultaneous approximation in L1(µ,X)

José Mendoza, Tijani Pakhrou

• Let X be a Banach space, (O,S,µ) a finite measure space, and L1(µ,X) the Banach space of X-valued Bochner µ-integrable functions defined on O endowed with its usual norm. Let us suppose that S0 is a sub-s-algebra of S, and let µ0 be the restriction of µ to S0. Given a natural number n, let N be a monotonous norm in . It is shown that if X is reflexive then L1(µ0,X) is N-simultaneously proximinal in L1(µ,X) in the sense of Fathi et al.