Remotal Sets in the Space of P-Integrable Functions

Abstract

Let X be a Banach space and G be a closed bounded subset of X. For x ∈ X, we set ρ(x,G) = sup {‖ x - y ‖ : y ∈ G} . The set G is called remotal if for any x ∈ X, there exists g ∈ G such that ρ(x,G) = ‖ x - g ‖. In this paper we show that for a separable remotal set G ⊂ X, the set of p-Bochner integrable functions, L^p(I,G) is in remotal L^p(I,X): Some other results are presented.

Key words and phrases. Aproximation, remotal sets.

2000 Mathematics Subject Classification. Primary: 46B20, Secondary: 46E40