Allan M Sinclair

C*-algebras nearly contained in type I algebras

In this paper we consider near inclusions $A\subseteq_γB$ of C$^*$-algebras. We show that if $B$ is a separable type I C*-algebra and $A$ satisfies Kadison's similarity problem, then $A$ is also type I and use this to obtain an embedding of $A$ into $B$.