On the Index and Dilations of Completely Positive Semigroups
نویسندگان
چکیده
It is known that every semigroup of normal completely positive maps P = {Pt : t ≥ 0} of B(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0-semigroup acting on B(K) for some Hilbert space K ⊇ H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator
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