Geodesic
Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction
Documenta mathematica, Tome 22 (2017), pp. 1375-1466.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 47L60, 46L55
Keywords: unbounded operator, regular Hilbert module operator, integrable representation, induction of representations, graded $^\ast$-algebra, Fell bundle, C$^\ast$-algebra generated by unbounded operators, C$^\ast$-envelope, C$^\ast$-hull, host algebra, Weyl algebra, canonical commutation relations, local-global principle, Rieffel deformation 
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     author = {Meyer, Ralf},
     title = {Representations of $^\ast${-Algebras} by {Unbounded} {Operators:} {C}$^\ast${-Hulls,} {Local-Global} {Principle,} and {Induction}},
     journal = {Documenta mathematica},
     pages = {1375--1466},
     publisher = {mathdoc},
     volume = {22},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a9/}
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Meyer, Ralf. Representations of $^\ast$-Algebras by Unbounded Operators: C$^\ast$-Hulls, Local-Global Principle, and Induction. Documenta mathematica, Tome 22 (2017), pp. 1375-1466. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a9/