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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).
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) alon...
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