Li K, Nowak P, Spakula J, Zhang J (2021)
Publication Type: Journal article
Publication year: 2021
Book Volume: 15
Pages Range: 655-682
Journal Issue: 2
DOI: 10.4171/GGD/610
In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic expanders. We show that being a sequence of asymptotic expanders is a coarse property under certain connectedness condition, and it implies non-uniformly local amenability. Moreover, we also analyse some C *-algebraic properties of uniform quasi-local algebras. In particular, we show that a uniform quasi-local algebra is nuclear if and only if the underlying metric space has Property A.
APA:
Li, K., Nowak, P., Spakula, J., & Zhang, J. (2021). Quasi-local algebras and asymptotic expanders. Groups Geometry and Dynamics, 15(2), 655-682. https://doi.org/10.4171/GGD/610
MLA:
Li, Kang, et al. "Quasi-local algebras and asymptotic expanders." Groups Geometry and Dynamics 15.2 (2021): 655-682.
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