Topologies on dual spaces
The dual space of a locally compact group G carries the Fell topology defined in Definition 1.67 with the closure operation given in Proposition 1.68. This topology is important for investigating the L1- and C*-algebras of G. As we have seen in Chapter 4, for many groups Mackey’s theory enables us to determine as a set. The basic tools are inducing representations of closed subgroups up to G and restricting representations to closed subgroups.
However, even when starting with irreducible representations, neither inducing ...