Convergence sets in reflexive Banach spaces

Abstract:

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