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Normal Extensions of Representations of Abelian Semigroups

Published online by Cambridge University Press:  20 November 2018

Boyu Li
Boyu Li*
Affiliation:
Pure Mathematics Department, University of Waterloo, Waterloo, ON, N2L–3G1 e-mail: [email protected]
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Abstract

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A commuting family of subnormal operators need not have a commuting normal extension. We study when a representation of an abelian semigroup can be extended to a normal representation, and show that it suffices to extend the set of generators to commuting normals. We also extend a result due to Athavale to representations on abelian lattice ordered semigroups.

Keywords

47B2047A2047D03subnormal operatornormal extensionregular dilationlattice ordered semigroup
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 564 - 574
Copyright
Copyright © Canadian Mathematical Society 2016

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