Reduction Theory on the Relative Entropy, II

Let M⊃N be a pair of von Neumann algebras of finite type and L denotes the algebra generated by N and the center Z(M) of M. Then, the formula H(M|N)=H(M|L) +H(L|N) is shown to hold, where H(・|・)is the relative entropy in Pimsner-Popa's sense. This fact makes it possible to compute the relative entropy H(M|N) for any pair M⊃N of von Neumann algebras of finite type