Sufficient subalgebras and the relative entropy of states of a von Neumann algebra |
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| Authors: | Dénes Petz |
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| Affiliation: | (1) Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, D-7400 Tübingen, Federal Republic of Germany;(2) Present address: Mathematical Institute of HAS, Reáltanoda u. 13–15, P.O. Box. 127, H-1364 Budapest, Hungary |
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| Abstract: | A subalgebraM0 of a von Neumann algebraM is called weakly sufficient with respect to a pair ( , ) of states if the relative entropy of and coincides with the relative entropy of their restrictions toM0. The main result says thatM0 is weakly sufficient for (,) if and only ifM0 contains the Radon-Nikodym cocycle [D,D]t. Other conditions are formulated in terms of generalized conditional expectations and the relative Hamiltonian. |
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