A non spatial continuous semigroup of *-endomorphisms of \({\mathcal B}({\mathcal H})\)
In his paper ``An index theory fo semigroups of *-endomorphisms of B(\({\mathcal B})\) and type II, factors'' [Can. J. Math. 40, No.1, 86-114 (1988; Zbl 0632.46048)], \textit{R. Powers} associated an index with continuous one parameter semigroups \(\alpha_ t\) of *-endomorphisms of B(\({\mathcal B})\) having an interwining semigroup of isometrics, that is, there is strongly continuous semigroup of isometrics U(t)\(\in B({\mathcal B})\) so that \(U(t)A=\alpha_ t(A)U(t)\) for all \(A\in B({\mathcal B})\). He raised the question of whether such an intertwining semigroup of isometrics always exists. In this paper he constructs a continuous one parameter semigroup \(\alpha_ t\) of *-endomorphisms of B(\({\mathcal B})\) having the property that there does not exist a strongly continuous one parameter semigroup of intertwining isometrics. The construction is technical and uses quasi-free states of CAR algebras and almost multiplication operators.
continuous one parameter semigroup of intertwining isometrics
scientific article; zbMATH DE number 4061983