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C*–algebras Nearly Contained in Type I Algebras
Published online by Cambridge University Press: 20 November 2018
Abstract
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
$B$.
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- Copyright © Canadian Mathematical Society 2013