Positive definite class functions on a topological group and characters of factor representations (Q818032)

This paper concerns the general theory of representations of a Hausdorff topological group \(G\). It consists of two parts. The first one is dedicated to the study of continuous positive definite functions \(f\in {\mathcal{P}}(G)\) on \(G\) and continuous unitary representations \((=UR)\) \(\pi\) of \(G\). The second part deals with several weak topologies and also the compact uniform topology on \({\mathcal{P}}(G)\) and some of its subsets. The authors establish three important theorems (Theorems A, B, D) (note that for a fourth one (Theorem C), a counterexample was found).