Best p-simultaneous approximation in Köthe Bochner Function Spaces

Abstract

Let (T, ∑ , μ) be a finite complete measure space and X a real Banach space. For p a real number in [1,∞) , the lp sum of the real n-Tuple x = (xi)n i=1 is defined by the norm kxk = ∑ n i=1 |xi|p. A characterization of best simultaneous approximation of Köthe Bochner function spaces in the lp sum sense is given. This characterization is a generalization of some analogous theorems for Lp Bochner spaces and the Orlicz Bochner spaces.