Vol. 80, No. 1, 1979

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A Radon-Nikodým theorem for -algebras

Stanley P. Gudder

Vol. 80 (1979), No. 1, 141–149
Abstract

A noncommutative Radon-Nikodym theorem is developed in the context of -algebras. Previous results in this direction have assumed a dominance condition which results in a bounded “Radon-Nikodym derivative”. The present result achieves complete generality by only assuming absolute continuity and in this case the “Radon-Nikodym derivative” may be unbounded. A Lebesgue decomposition theorem is established in the Banach -algebra case.

Mathematical Subject Classification 2000
Primary: 46L50, 46L50
Secondary: 46K05
Milestones
Received: 24 February 1978
Revised: 13 July 1978
Published: 1 January 1979
Authors
Stanley P. Gudder