# Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction

### Ralf Meyer

Mathematisches Institut, Universität Göttingen, Bunsenstrasse3-5, 37073 Göttingen, Germany

## Abstract

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.

## Cite this article

Ralf Meyer, Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction. Doc. Math. 22 (2017), pp. 1375–1466

DOI 10.4171/DM/600