Geodesic
Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction
Documenta mathematica, Tome 22 (2017), pp. 1375-1466
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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.
DOI : 10.4171/dm/600
Classification : 46L55, 47L60
Mots-clés : local-global principle, host algebra, unbounded operator, regular Hilbert module operator, integrable representation, induction of representations, graded ∗-algebra, Fell bundle, C∗-algebra generated by unbounded operators, C∗-envelope, C∗-hull, Weyl algebra, canonical commutation relations, Rieffel deformation 
@article{10_4171_dm_600,
     author = {Ralf Meyer},
     title = {Representations of $^\ast${-Algebras} by {Unbounded} {Operators:} {C}$^\ast${-Hulls,} {Local-Global} {Principle,} and {Induction}},
     journal = {Documenta mathematica},
     pages = {1375--1466},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/600},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/600/}
}
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Ralf Meyer. Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction. Documenta mathematica, Tome 22 (2017), pp. 1375-1466. doi: 10.4171/dm/600

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