Mathematics – Functional Analysis
Scientific paper
2010-06-27
Mathematics
Functional Analysis
15 pages. Some additional reference is given. Proof of Proposition 2.1 (iv) is corrected
Scientific paper
Let $\cla$ be a matrix algebra over real or complex field. The set of trace preserving unital completely positive maps $CP_{\phi}$ on $\cla$ form a compact convex subset of an Euclidean space. The main result says that an ergodic element in the boundary of $CP_{\phi}$ belongs to a convex open subset of the boundary and thus can not be an extremal element in $CP_{\phi}$. These results made it possible to have a reduction algorithm to find extremal elements of $CP_{\phi}$ in the lower dimensional faces made of completely reduced non-ergodic elements.
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