Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One
Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One
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DOI：
10.1090/s0002-9947-2011-05431-0
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发表时间：
2008-01
期刊：
影响因子：
--
通讯作者：
Huaxin Lin
中科院分区：
文献类型：
--
作者：
Huaxin Lin
Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple C*-algebra with tracial rank no more than one. Suppose that $\phi, \psi: C\to A$ are two unital monomorphisms. With some restriction on $C,$ we show that $\phi$ and $\psi$ are approximately unitarily equivalent if and only if [\phi]=[\psi] in KL(C,A) \tau\circ \phi=\tau\circ \psi for all tracial states of A and \phi^{\ddag}=\psi^{\ddag}, here \phi^{\ddag} and \psi^{\ddag} are homomorphisms from $U(C)/CU(C)\to U(A)/CU(A) induced by \phi and \psi, respectively, and where CU(C) and CU(A) are closures of the subgroup generated by commutators of the unitary groups of C and B.
