Expectations in semifinite algebras

Sterling K. Berberian

Vol. 106 (1983), No. 1, 33–43

DOI: 10.2140/pjm.1983.106.33

Abstract

Every semifinite von Neumann algebra A possesses an expectation ♮ : A → W, where W is a commutative von Neumann subalgebra of A containing the center of A, and where ♮ extends the trace of a “large” finite subalgebra of A. An AW^∗-algebraic proof yields applications to the embedding of semifinite AW^∗-algebras in algebras of type I.

Mathematical Subject Classification 2000

Primary: 46L05

Milestones

Received: 5 March 1982

Revised: 12 April 1982

Published: 1 May 1983