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Journal of Operator Theory

Volume 78, Issue 1,  Summer  2017  pp. 89-117.

Composition of topological correspondences

Authors:  Rohit Dilip Holkar
Author institution: Department of Mathematics, Federal University of Santa Catarina, Florianopolis, 88. 040-900, Brazil and Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, NCL Colony, Pashan, Pune 411008, India

Summary:  In our previous work, \textit{J. Operator Theory}, \textbf{77}(2017), 217--241, we define a topological correspondence from a locally compact groupoid equipped with a Haar system to another one and we show that a topological correspondence, $(X,\lambda)$, from a locally compact groupoid with a Haar system $(G,\alpha)$ to another one, $(H,\beta)$, produces a $C^*$-correspondence $\mathcal{H}(X)$ from $C^*(G,\alpha)$ to $C^*(H,\beta)$. 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.

Keywords:  topological correspondences, composition of topological correspondences, functoriality of topological correspondences

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