Linear Radon-Nikodym Theorems for States on A Von Neumann Algebra

Abstract

Several linear Radon-Nikodym theorems for states on a von Neumann algebra are obtained in the context of a one parameter family of positive cones introduced by H. Araki. Among other results, we determine when a normal state φ admits a linear Radon-Nikodym derivative with respect to a distinguished normal faithful state φ0 in the sense of Sakai, that is, φ=hφ0+φ0h with a positive h in the algebra. © 1982, Research Institute forMathematical Sciences. All rights reserved.