C*-algebras nearly contained in type I algebras

Abstract

In this paper we consider near inclusions $A{\subseteq }_{\gamma }B$ of C${}^{\ast }$-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 $B$.

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