Composition of topological correspondences

Abstract

In the previous article, we proved that a topological correspondence $(X,\lambda )$ from a locally compact groupoid with a Haar system $(G,\alpha )$ to another one, $(H,\beta )$, produces a $C^{\ast }$-correspondence $\mathcal{H}(X)$ from $C^{\ast }(G,\alpha )$ to $C^{\ast }(H,\beta )$. In the present article, we describe how to form a composite of two topological correspondences when the bispaces are Hausdorff and second countable in addition to being locally compact.

arXiv comment21 pages, 5 Figures. Added a new reference ([4]), some typos corrected. An altered version of this article is accepted for publication in the Journal of Operator Theory