Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
Abstract
A subalgebra M 0 of a von Neumann algebra M is called weakly sufficient with respect to a pair (φ,ω) of states if the relative entropy of φ and ω coincides with the relative entropy of their restrictions to M 0. The main result says that M 0 is weakly sufficient for (φ,ω) if and only if M 0 contains the Radon-Nikodym cocycle [ Dφ, Dω] t . Other conditions are formulated in terms of generalized conditional expectations and the relative Hamiltonian.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- March 1986
- DOI:
- 10.1007/BF01212345
- Bibcode:
- 1986CMaPh.105..123P