Earlier definition of the relative entropy of two faithful normal positive linear functionals of a von Neumann algebra is generalized to non-faithful functionals. Basic properties of the relative entropy are proved for this generalization.
Cite this article
Huzihiro Araki, Relative Entropy for States of von Neumann Algebras II. Publ. Res. Inst. Math. Sci. 13 (1977), no. 1, pp. 173–192DOI 10.2977/PRIMS/1195190105