Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415222 | Journal of Functional Analysis | 2014 | 38 Pages |
Abstract
Let A be a unital separable simple Z-stable Câ-algebra which has rational tracial rank at most one and let uâU0(A), where U0(A) is the connected component of the unitary group of A containing the identity. We show that, for any ϵ>0, there exists a self-adjoint element hâA such that(0.1)âuâexp(ih)â<ϵ. But there is no control of âhâ in general. Let CU(A) be the closure of the commutator subgroup of the unitary group of A and let uâCU(A). We prove that there exists a self-adjoint element hâA such that(0.2)âuâexp(ih)â<ϵandâhâ⩽2Ï. Examples are given that the bound 2Ï for âhâ is optimal in general. For the Jiang-Su algebra Z, we show that, if uâU0(Z) and ϵ>0, there exists a real number âÏ
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Huaxin Lin,