Simultaneous proximinality in \(L^{\infty}(\mu,X)\)
DOI:
https://doi.org/10.33993/jnaat422-984Keywords:
simultaneous approximation, Banach spacesAbstract
Let \(X\) be a Banach space and \(G\) be a closed subspace of \(X\). Let us denote by \(L^{\infty}\left( \mu,X\right) \) the Banach space of all \(X\)-valued essentially bounded functions on a \(\sigma\)-finite complete measure space \(\left( \Omega,\Sigma,\mu\right) .\) In this paper we show that if \(G\) is separable, then \(L^{\infty}\left( \mu,G\right) \) is simultaneously proximinal in \(L^{\infty}\left( \mu,X\right) \) if and only if \(G\) is simultaneously proximinal in \(X.\)Downloads
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