Sufficient Subalgebras and the Relative Entropy of States of a von Neumann Algebra
نویسندگان
چکیده
A subalgebra Mo 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 Mo. The main result says that Mo is weakly sufficient for (φ, ω) if and only if Mo contains the RadonNikodym cocycle [Dφ,Dω]t. Other conditions are formulated in terms of generalized conditional expectations and the relative Hamiltonian.
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