The tracial topological rank of extensions of $C^*$-algebras
Keyword(s):
Let $0\to \mathcal J\to \mathcal A\to \mathcal A / \mathcal J\to 0$ be a short exact sequence of separable $C^*$-algebras. We introduce the notion of tracially quasidiagonal extension. Suppose that $\mathcal J$ and $\mathcal A/J$ have tracial topological rank zero. We prove that if $(\mathcal A, \mathcal J)$ is tracially quasidiagonal, then $\mathcal A$ has tracial topological rank zero.
2003 ◽
Vol 46
(3)
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pp. 388-399
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Keyword(s):
2005 ◽
Vol 48
(3)
◽
pp. 673-690
2004 ◽
Vol 125
(1)
◽
pp. 91-119
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Keyword(s):
Linear orthogonality preservers of Hilbert $C^{*}$-modules over $C^{*}$-algebras with real rank zero
2012 ◽
Vol 140
(9)
◽
pp. 3151-3160
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1997 ◽
Vol 125
(9)
◽
pp. 2671-2676