Convergence sets in reflexive Banach spaces

Abstract

A closed linear subspace M M of a reflexive Banach space X X with X X and X ∗ {X^ \ast } strictly convex is the range of a linear contractive projection iff J ( M ) J(M) is a linear subspace of X ∗ {X^ \ast } . Hence the convergence set of a net of linear contractions is the range of a contractive projection if X X and X ∗ {X^ \ast } are locally uniformly convex.