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Normal Extensions of Representations of Abelian Semigroups

  Published:2016-05-31
 Printed: Sep 2016
  • Boyu Li,
    Pure Mathematics Department , University of Waterloo , Waterloo, ON , Canada N2L--3G1
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Abstract

A commuting family of subnormal operators need not have a commuting normal extension. We study when a representation on 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: subnormal operator, normal extension, regular dilation, lattice ordered semigroup subnormal operator, normal extension, regular dilation, lattice ordered semigroup
MSC Classifications: 47B20, 47A20, 47D03 show english descriptions Subnormal operators, hyponormal operators, etc.
Dilations, extensions, compressions
Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
47B20 - Subnormal operators, hyponormal operators, etc.
47A20 - Dilations, extensions, compressions
47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}
 

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