Minimizing the relative entropy in a face

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Original languageEnglish
Pages (from-to)7-14
Number of pages8
JournalLett. Math. Phys.
Volume19
Issue number1
Publication statusPublished - 1990

Abstract

For a separating state -algebra A, we give a limit formula for the minimal relative entropy S(.) in any face, as well as for the unique minimizer. In terms of this minimum, we define a superadditive function rho on the faces of A. In the case of a W*-algebra and normal rho can be considered as a function on the projection lattice. We show that the largest additive function on the projection lattice of an abelian W*-subalgebra, which is dominated by rho, is given by a normal positive, but not necessarily normalized linear functional on A. This functional is the unique solution of a minimal entropy problem.

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Minimizing the relative entropy in a face. / Raggio, G. A.; Werner, R. F.
In: Lett. Math. Phys., Vol. 19, No. 1, 1990, p. 7-14.

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Raggio GA, Werner RF. Minimizing the relative entropy in a face. Lett. Math. Phys. 1990;19(1):7-14. doi: 10.1007/BF00402255
Raggio, G. A. ; Werner, R. F. / Minimizing the relative entropy in a face. In: Lett. Math. Phys. 1990 ; Vol. 19, No. 1. pp. 7-14.
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