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| Some Properties of Tracially Quasidiagonal Extensions |
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Citation： |
Yile ZHAO,Xiaochun FANG,Xiaoming XU.Some Properties of Tracially Quasidiagonal Extensions[J].Chinese Annals of Mathematics B,2019,40(1):97~110 |
| Page view： 1239
Net amount： 795 |
Authors： |
Yile ZHAO; Xiaochun FANG;Xiaoming XU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11871375, 11371279, 11601339) and
Zhejiang Provincial Natural Science Foundation of China
(No.LY13A010021). |
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| Abstract： |
Suppose that $
0 \xrightarrow{}I \xrightarrow{
} A \xrightarrow{} A/I
\xrightarrow{} 0$ is a tracially quasidiagonal extension of $C^*$-algebras. In this paper,
the authors
give two descriptions of the $K_0$, $K_1$ index maps which are induced by the above extension and
show that for any $\epsilon>0$, any $\tau$ in the tracial state
space of $A/I$ and any projection $\ov{p}\in A/I$ (any unitary
$\ov{u}\in A/I$), there exists a projection $p\in A$ (a unitary
$u\in A$) such that $|\tau(\ov{p})-\tau(\pi(p))|<\epsilon$
($|\tau(\ov{u})-\tau(\pi(u))|<\epsilon$). |
Keywords： |
Tracially topological rank, Quasidiagonal extension, Tracially quasidiagonal extension |
Classification： |
46L05, 46L35 |
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