Abstract
We show that the partial crossed product of a commutative C∗-algebra by an exact discrete group is nuclear if the full and reduced partial crossed products coincide. This generalises a result by Matsumura for global actions. In general, we prove that a partial action of an exact discrete group on a C∗-algebra A has Exel's approximation property if and only if the full and reduced crossed products by the diagonal partial action on A⊗maxAop coincide. We apply our results to show that the weak containment property implies nuclearity in the case of semigroup C∗-algebras and C∗-algebras of separated graphs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
