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Journal of Convex Analysis 21 (2014), No. 2, 307--316
Copyright Heldermann Verlag 2014

Relative Chebyshev Centers in L(μ,X)

Tijani Pakhrou
Dept. of Mathematical Analysis, Faculty of Sciences, University of Alicante, 03080 Alicante, Spain


Let $X$ be a Banach space and $Y$ a weakly $\mathcal{K}$-analytic subspace of $X$. In this paper we study the simultaneous proximinality in the space $L_\infty(\mu,X)$. In this sense we have proved that $L_\infty(\mu,Y)$ is simultaneously proximinal in $L_\infty(\mu,X)$ if, and only if, $Y$ is simultaneously proximinal in $X$.

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