Contractive projections on an s1 space

Abstract

This paper discusses the class of contractive (operator norm one) projections on the complex s1 space of a probability measure. In particular there is a characterization of such projections and of their range spaces, and also of the closed vector sublattices of s1 and the subspaces of s1 that are isometrically isomorphic to some s1 space. Further results include an extension of the above results to more general measure spaces and several results about contraction operators on s1. © 1965 by Pacific Journal of Mathematics.