TY - JOUR

T1 - Minimizing the relative entropy in a face

AU - Raggio, G. A.

AU - Werner, R. F.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

U2 - 10.1007/BF00402255

DO - 10.1007/BF00402255

M3 - Article

VL - 19

SP - 7

EP - 14

JO - Lett. Math. Phys.

JF - Lett. Math. Phys.

SN - 1573-0530

IS - 1

ER -