Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Limit operator theory for groupoids


Authors: Kyle Austin and Jiawen Zhang
Journal: Trans. Amer. Math. Soc. 373 (2020), 2861-2911
MSC (2010): Primary 47A53; Secondary 22A22, 46L55
DOI: https://doi.org/10.1090/tran/8005
Published electronically: January 28, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We extend the symbol calculus and study the limit operator theory for $ \sigma $-compact, étale, and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact groups and discrete metric spaces with Property A, but also establish new limit operator theories for group/groupoid actions and uniform Roe algebras of groupoids. In the process, we extend a monumental result by Exel, Nistor, and Prudhon, showing that the invertibility of an element in the groupoid $ C^*$-algebra of a $ \sigma $-compact amenable groupoid with a Haar system is equivalent to the invertibility of its images under regular representations.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 47A53, 22A22, 46L55

Retrieve articles in all journals with MSC (2010): 47A53, 22A22, 46L55


Additional Information

Kyle Austin
Affiliation: Weizmann Institute of Science and Technology, Department of Mathematics, 234 Herzl Street, POB 26, Rehovot 7610001, Israel
Email: ksaustin88@gmail.com

Jiawen Zhang
Affiliation: University of Southampton, School of Mathematics, Building 54, Highfield, Southampton SO17 1BJ, United Kingdom
Email: jiawen.zhang@soton.ac.uk

DOI: https://doi.org/10.1090/tran/8005
Received by editor(s): April 25, 2019
Received by editor(s) in revised form: September 11, 2019
Published electronically: January 28, 2020
Additional Notes: The first author was supported by the Israeli Science Foundation grants ISF-Moked grant 2095/15 and grant No. 522/14.
The second author was supported by the Sino-British Trust Fellowship by Royal Society, International Exchanges 2017 Cost Share (China) grant EC$$NSFC$$170341, NSFC11871342, and NSFC11811530291.
Article copyright: © Copyright 2020 American Mathematical Society