Topological construction of $C^*$-correspondences for groupoid $C^*$-algebras

Rohit Dilip Holkar

Topological construction of $C^$-correspondences for groupoid $C^$-algebras

Operator Algebras 2016-08-26 v2 Functional Analysis

Authors: Rohit Dilip Holkar

Abstract

Let $(G,\alpha)$ and $(H,\beta)$ be locally compact groupoids with Haar systems. We define a topological correspondence from $(G,\alpha)$ to $(H,\beta)$ to be a $G$ - $H$ -bispace $X$ on which $H$ acts properly and $X$ carries a continuous family of measures which is $H$ -invariant and each measure in the family is $G$ -quasi invariant. We show that a topological correspondence produces a $C^*$ -correspondence from $C^*(G,\alpha)$ to $C^*(H,\beta)$ . We give many examples of topological correspondences.

Keywords

groupoid C*-algebra topological correspondence C*-correspondence Haar system locally compact groupoid bispace quasi-invariant measure

Cite

@article{arxiv.1510.07534,
  title  = {Topological construction of $C^*$-correspondences for groupoid $C^*$-algebras},
  author = {Rohit Dilip Holkar},
  journal= {arXiv preprint arXiv:1510.07534},
  year   = {2016}
}

Comments

This version has 24 pages; the case of groupoid equivalence is removed from Section 2.1. A modified version of this article is accepted for publication in Journal of Operator Theory