Convergence sets in reflexive Banach spaces
Abstract: A closed linear subspace of a reflexive Banach space with and strictly convex is the range of a linear contractive projection iff is a linear subspace of . Hence the convergence set of a net of linear contractions is the range of a contractive projection if and are locally uniformly convex.
Keywords: Strictly convex, locally uniformly convex, contractive projection, convergence set, mean ergodic theorem
Article copyright: © Copyright 1975 American Mathematical Society