Representations of \(^\ast\)-algebras by unbounded operators: C\(^\ast\)-hulls, local-global principle, and induction (Q683765)

Summary: We define a C\(^\ast\)-hull for a \(^\ast\)-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\(^\ast\)-hull for a certain class of integrable representations of a graded \(^\ast\)-algebra, given a C\(^\ast\)-hull for its unit fibre.