# Linear Radon-Nikodym Theorems for States on a von Neumann Algebra

### Hideki Kosaki

University of Kansas, Lawrence, USA

## 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 _ϕ_0 in the sense of Sakai, that is, *ϕ* = _h ϕ_0 + _ϕ_0 *h* with a positive *h* in the algebra.

## Cite this article

Hideki Kosaki, Linear Radon-Nikodym Theorems for States on a von Neumann Algebra. Publ. Res. Inst. Math. Sci. 18 (1982), no. 1, pp. 379–386

DOI 10.2977/PRIMS/1195184028