Normal Extensions of Representations of Abelian Semigroups

Canadian mathematical bulletin

Boyu Li¹ 

[1] Pure Mathematics Department , University of Waterloo , Waterloo, ON , Canada N2L--3G1

关键词: subnormal operator;    normal extension;    regular dilation;    lattice ordered semigroup;   

DOI  :  10.4153/CMB-2016-021-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 torepresentations on abelian lattice ordered semigroups.

【 授权许可】

Unknown