2019/03/20 by Kyle Austin, Jiawen Zhang, Austin, Kyle +1
Mathematics · #46L55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Primary 47A53 #Secondary 22A22
paper · pdf · doi:10.48550/arxiv.1903.08442
openalex publication_date 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the symbol calculus and study the limit operator theory for σ-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 σ-compact amenable groupoid with a Haar system is equivalent to the invertibility of its images under regular representations.