Relative Chebyshev Centers in L∞(μ,X)

Let X be a Banach space and Y a weakly K-analytic subspace of X. In this paper we study the simultaneous proximinality in the space L∞(μ,X). In this sense we have proved that L∞(μ, Y) is simultaneously proximinal in L∞(μ,X) if, and only if, Y is simultaneously proximinal in X.Research partially supported by MTM 2012-31286 (Spanish Ministry of Economy and Competitiveness) and GRE11-23 (University of Alicante, Spain)