Asymptotic Stability I : Completely Positive Maps

@inproceedings{Arveson2003AsymptoticSI,
  title={Asymptotic Stability I : Completely Positive Maps},
  author={William Arveson},
  year={2003}
}
We show that for every “locally finite” unit-preserving completely positive map P acting on a C∗-algebra, there is a corresponding ∗-automorphism α of another unital C∗-algebra such that the two sequences P, P , P , . . . and α, α, α, . . . have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps on von Neumann algebras, as well as for one-parameter semigroups. These results are operator algebraic… CONTINUE READING

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