The similarity problem for representations of $C\sp{\ast} $-algebras

John W. Bunce
1981 Proceedings of the American Mathematical Society  
Let it: A -* B(H) be a bounded homomorphism of a C*-algebra into the bounded operators on a Hubert space. We prove that, if it is cyclic, there is a •-representation 9: A -» B(H) and a bounded one-to-one positive operator P such that P6(a) = it(d)P. We include applications to 0-derivations and invariant operator ranges for operator algebras.
doi:10.1090/s0002-9939-1981-0597652-0 fatcat:hsbohp6b7ba3zn3cx7xgterz5q