5 citations · 13 across the 6 of their papers we have counts for
7 papers
Limit operator theory for groupoids
Kyle Austin, Jiawen Zhang
We extend the symbol calculus and study the limit operator theory for -compact, étale and amenable groupoids, in the Hilbert space case. This approach not only unifies various e…
Groupoid Models of -algebras and Gelfand Duality
Kyle Austin, Atish Mitra
We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce -morphisms of maximal and minimal groupoid -algebras. We show that the as…
Inverse Systems of Groupoids, with Applications to Groupoid -algebras
Kyle Austin, Magdalena C. Georgescu
We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between t…
Higson Compactification and Dimension Raising
Kyle Austin, Žiga Virk
Let and be proper metric spaces. We show that a coarsely -to- map induces an -to- map of Higson coronas. This viewpoint turns out to be success…
Scale Structures and C*-algebras
Kyle Austin, Jerzy Dydak, Michael Holloway
The purpose of this paper is to investigate the duality between large scale and small scale. It is done by creating a connection between C*-algebras and scale structures. In the co…
Discreteness and Large Scale Surjections
Kyle Austin
We study the concept of coarse disjointness and large scale -to- functions. As a byproduct, we obtain an Ostrand-type characterization of asymptotic dimension for coarse stru…
Partitions of unity and coverings
Kyle Austin, Jerzy Dydak
The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existe…