Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One

Details Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One

2008-01-18

arxiv.org/abs/0801.2929v4

Mathematics

Operator Algebras

66 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximate Unitary Equivalence in Simple C^*-algebras of Tracial Rank One will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-691415