Representations of *-algebras by unbounded operators: C*-hulls, local-global principle, and induction

We define a C*-hull for a -algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable representations on Hilbert modules through the integrable representations on Hilbert spaces. The induction theorem constructs a C-hull for a certain class of integrable representations of a graded -algebra, given a C-hull for its unit fibre.