Proximinality and unicity in vector-valued function spaces

Abstract

Let (I, μ) be a given finite measure space. If X is a Banach space, we set L ^p (I X) to denote the Banach space of p-Bochner integrable functions. It is the object of this paper to discuss unicity and proximinality of L ^p (I G) in L ^p (I X), where G is a closed subspace of X. Further, we generalize the work of Kroo on unicity in vector-valued function spaces. Some other results are presented.