ISSN:
1573-0530
Keywords:
46L30
;
81C99
;
49A40
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract For a separating state ρ of a C *-algebra A, we give a limit formula for the minimal relative entropy S(ρ, ·) in any face, as well as for the unique minimizer. In terms of this minimum, we define a superadditive function $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\rho } $$ on the faces of A. In the case of a W *-algebra and normal ρ, $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\rho } $$ can be considered as function on the projection lattice of an abelian W *-subalgebra, which is dominated by $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\rho } $$ , 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00402255
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