Sufficient subalgebras and the relative entropy of states of a von Neumann algebra |
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| Authors: | Dénes Petz |
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| Institution: | (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 subalgebraM
0 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 toM
0. The main result says thatM
0 is weakly sufficient for (,) if and only ifM
0 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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| Keywords: | |
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