Vol. 15, No. 2, 1965

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Contractive projections on an L1 space

Ronald George Douglas

Vol. 15 (1965), No. 2, 443–462

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
Received: 6 February 1964
Published: 1 June 1965
Ronald George Douglas