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# C$^*$-algebras Nearly Contained in Type $\mathrm{I}$ Algebras

Published:2012-03-24
Printed: Feb 2013
• Erik Christensen,
Institute for Mathematiske Fag, University of Copenhagen, Copenhagen, Denmark
• Allan M. Sinclair,
School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland
• Roger R. Smith,
Department of Mathematics, Texas A{\&}M University, College Station TX 77843-3368, U.S.A.
• Stuart White,
School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow Q12 8QW, Scotland
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## Abstract

In this paper we consider near inclusions $A\subseteq_\gamma B$ of C$^*$-algebras. We show that if $B$ is a separable type $\mathrm{I}$ C$^*$-algebra and $A$ satisfies Kadison's similarity problem, then $A$ is also type $\mathrm{I}$ and use this to obtain an embedding of $A$ into $B$.
 Keywords: C$^*$-algebras, near inclusions, perturbations, type I C$^*$-algebras, similarity problem
 MSC Classifications: 46L05 - General theory of $C^*$-algebras