C*–algebras Nearly Contained in Type I Algebras
Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 52-65
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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 $B$ .
Mots-clés :
46L05, 46L45, C*-algebras, near inclusions, perturbations, type I C*-algebras, similarity problem
Christensen, Erik; Sinclair, Allan M.; Smith, Roger R.; White, Stuart. C*–algebras Nearly Contained in Type I Algebras. Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 52-65. doi: 10.4153/CJM-2012-001-1
@article{10_4153_CJM_2012_001_1,
author = {Christensen, Erik and Sinclair, Allan M. and Smith, Roger R. and White, Stuart},
title = {C*{\textendash}algebras {Nearly} {Contained} in {Type} {I} {Algebras}},
journal = {Canadian journal of mathematics},
pages = {52--65},
year = {2013},
volume = {65},
number = {1},
doi = {10.4153/CJM-2012-001-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-001-1/}
}
TY - JOUR AU - Christensen, Erik AU - Sinclair, Allan M. AU - Smith, Roger R. AU - White, Stuart TI - C*–algebras Nearly Contained in Type I Algebras JO - Canadian journal of mathematics PY - 2013 SP - 52 EP - 65 VL - 65 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-001-1/ DO - 10.4153/CJM-2012-001-1 ID - 10_4153_CJM_2012_001_1 ER -
%0 Journal Article %A Christensen, Erik %A Sinclair, Allan M. %A Smith, Roger R. %A White, Stuart %T C*–algebras Nearly Contained in Type I Algebras %J Canadian journal of mathematics %D 2013 %P 52-65 %V 65 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-001-1/ %R 10.4153/CJM-2012-001-1 %F 10_4153_CJM_2012_001_1
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