Contractive projections on an L₁ space

Ronald George Douglas

Vol. 15 (1965), No. 2, 443–462

DOI: 10.2140/pjm.1965.15.443

Abstract

This paper discusses the class of contractive (operator norm one) projections on the complex L₁ 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 L₁ and the subspaces of L₁ that are isometrically isomorphic to some L₁ space. Further results include an extension of the above results to more general measure spaces and several results about contraction operators on L₁.

Mathematical Subject Classification

Primary: 46.35

Secondary: 47.25

Milestones

Received: 6 February 1964

Published: 1 June 1965