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C$^*$-algebras Nearly Contained in Type $\mathrm{I}$ Algebras
  Published:2012-03-24
 Printed: Feb 2013
Canadian Journal of Mathematics
  • 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 C$^*$-algebras, near inclusions, perturbations, type I C$^*$-algebras, similarity problem
MSC Classifications: 46L05 show english descriptions General theory of $C^*$-algebras 46L05 - General theory of $C^*$-algebras
 
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