Asymptotically unitary equivalence and asymptotically inner automorphisms
| dc.creator | Lin, Huaxin | |
| dc.date | 2007-03-20 | |
| dc.date | 2008-02-27 | |
| dc.date.accessioned | 2026-07-07T09:23:25Z | |
| dc.date.available | 2026-07-07T09:23:25Z | |
| dc.description | Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple \CA with tracial rank zero. Suppose that $ϕ_1, ϕ_2: C\to A$ are two unital monomorphisms. We show that there is a continuous path of unitaries $\{u_t: t\in [0, \infty)\}$ of $A$ such that $$ \lim_{t\to\infty}u_t^*ϕ_1(a)u_t=ϕ_2(a)\tforal a\in C $$ if and only if $[ϕ_1]=[ϕ_2]$ in $KK(C,A),$ $τ\circ ϕ_1=τ\circ ϕ_2$ for all $τ\in T(A)$ and the rotation map ${\tildeη}_{ϕ_1,ϕ_2}$ associated with $ϕ_1$ and $ϕ_2$ is zero. In particular, an automorphism $\af$ on a unital separable simple \CA $A$ in ${\cal N}$ with tracial rank zero is asymptotically inner if and only if $$ [\af]=[{\rm id}_A] \text{in} KK(A,A) $$ and the rotation map ${\tildeη}_{ϕ_1, ϕ_2}$ is zero. Let $A$ be a unital AH-algebra (not necessarily simple) and let $\af\in Aut(A)$ be an automorphism. As an application, we show that the associated crossed product $A\rtimes_{\af}\Z$ can be embedded into a unital simple AF-algebra if and only if $A$ admits a strictly positive $\af$-invariant tracial state. | |
| dc.description | This is a revision of 04/07 | |
| dc.identifier | https://arxiv.org/abs/math/0703610 | |
| dc.identifier | http://arxiv.org/abs/math/0703610 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155726 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L05, 46L35 | |
| dc.title | Asymptotically unitary equivalence and asymptotically inner automorphisms | |
| dc.type | text |