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.
Cite this article
Ralf Meyer, Representations of -Algebras by Unbounded Operators: C-Hulls, Local-Global Principle, and Induction. Doc. Math. 22 (2017), pp. 1375–1466DOI 10.4171/DM/600