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C*–algebras Nearly Contained in Type I Algebras

Published online by Cambridge University Press:  20 November 2018

Erik Christensen
Affiliation:
Institute for Mathematiske Fag, University of Copenhagen, Denmark, e-mail: echris@math.ku.dk
Allan M. Sinclair
Affiliation:
School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, e-mail: a.sinclair@ed.ac.uk
Roger R. Smith
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A., e-mail: rsmith@math.tamu.edu
Stuart White
Affiliation:
School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow Q12 8QW, Scotland, e-mail: stuart.white@glasgow.ac.uk
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Abstract

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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

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