Details
| Original language | English |
|---|---|
| Pages (from-to) | 7-14 |
| Number of pages | 8 |
| Journal | Lett. Math. Phys. |
| Volume | 19 |
| Issue number | 1 |
| Publication status | Published - 1990 |
Abstract
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In: Lett. Math. Phys., Vol. 19, No. 1, 1990, p. 7-14.
Research output: Contribution to journal › Article › Research › peer review
}
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 -