Grothendieck spaces in approximation theory

Abstract

Abstract : The purpose of this work is to study systematically a set of closed vector subspaces - Grothendieck subspaces - of (C sub zero) (T,X),T a locally compact Hausdorff topological space and X a real Banach space, analogous to Grothendieck's set of closed vector subspaces of (C sub zero) (T,R) along with two subsets - Kakutani-Stone and Weierstrass-Stone subspaces - analogous to the sets of closed vector sublattices and closed subalgebras of (C sub zero) (T,R), and to develop, subsequently, a theory of best approximation in (C sub zero) (T,X) by closed vector subspaces in these sets. (Author)