Abstract
In this paper we apply the Bishop-Phelps Theorem to show that if \(X\) is a Banach space and \(G\subseteq X\) is a maximal subspace so that \(G^\perp = \{x^* \in X^*\mid x^*(y) = 0; \forall y \in G\}\) is an L-summand in \(X^*\), then \(L^1(\Omega,G)\) is contained in a maximal proximinal subspace of \(L^1(\Omega,X)\).
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