Best N-Simultaneous Approximation in Lp(μ, X) . (12th July 2017) - Pakhrou, Tijani
Abstract : Let X be a Banach space. Let 1 ≤ p < ∞ and denote by L p ( μ, X ) the Banach space of all X -valued Bochner p -integrable functions on a certain positive complete σ -finite measure space ( Ω, Σ, μ ), endowed with the usual p -norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset W of X, the set L p ( μ, W ) is N -simultaneously proximinal in L p ( μ, X ) for any arbitrary monotonous norm N in R n .