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

Ralf Meyer

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

Operator Algebras 2019-04-30 v3

Authors: Ralf Meyer

Abstract

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.

Keywords

*-algebras unbounded operators C*-hulls local-global principle induction theorem Hilbert modules integrable representations

Cite

@article{arxiv.1607.04472,
  title  = {Representations of *-algebras by unbounded operators: C*-hulls, local-global principle, and induction},
  author = {Ralf Meyer},
  journal= {arXiv preprint arXiv:1607.04472},
  year   = {2019}
}

Comments

Some proofs corrected and notation changed, added/removed some results, different numbering of results again