Linear Radon-Nikodym theorems for states on a von Neumann algebra are obtained in the context of a one parameter family of positive cones. Especially, necessary and sufficient conditions for existence of linear Radon-Nikodym derivatives are investigated. In the natural cone case we consider Jordan Banach algebras.
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Bruno Iochum, Hideki Kosaki, Linear Radon-NIkodym Theorems for Linear Radon-NIkodym Theorems for on JEW and W* Algebras. Publ. Res. Inst. Math. Sci. 21 (1985), no. 6, pp. 1205–1222DOI 10.2977/PRIMS/1195178512