SIMULTANEOUS FARTHEST POINTS IN VECTOR VALUED FUNCTION SPACES

Abstract

Let X be a Banach space, (I, \mu) be a finite measure space and G be a closed bounded subset of X: Let \varphi be an increasing subadditive continuous function on [0, \infty) with \infty(0) = 0, let us denote by L^{\varphi}(I,X), the space of all X-valued strongly measurable functions on I with \int_I \varphi || f(t) || dt <= \infty. In this paper, we show that for a separable simultaneously remotal set G in X, L^{\varphi}(I,G) is simultaneously remotal in L^{\varphi}(I,X). Further, we study
Banach space X with subspace Y such that L^{\varphi}(I,B[Y])is remotal in L^{\varphi}(I,X), where B[Y ] is the unit ball of Y: