The Extension of Unital Completely Positive Semigroups on Operator Systems to Semigroups on $C^*$-algebras

DOI10.1134/S1995080222100389arXiv2206.09270MaRDI QIDQ6402478

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Publication date: 18 June 2022

Abstract: The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^{*}$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on operator systems. We show that any continuous unital completely positive semigroup on matricial system can be extended to a semigroup on a finite-dimensional $C^{*}$-algebra, which is an injective envelope of the matricial system. In case the semigroup is invertible, this extension is unique.

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Operator spaces and completely bounded maps (46L07) Operator spaces (= matricially normed spaces) (47L25) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

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