Similarity Problems, Følner Sets and Isometric Representations of Amenable Semigroups

  • Catalin BadeaEmail author
  • Laurian Suciu


We revisit Sz.-Nagy’s criteria for similarity of Hilbert space bounded linear operators to isometries or unitaries and present new ones. We also discuss counterparts of the Dixmier–Day theorem concerning bounded representations of amenable groups and semigroups. We highlight the role of Følner sets in similarity problems in both settings of unimodular, \(\sigma \)-compact, amenable groups and in discrete semigroups possessing the Strong Følner condition (SFC).


Operators similar to isometries unitarizable representations amenable semigroups Følner conditions 

Mathematics Subject Classification

47A05 47A15 43A07 



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Authors and Affiliations

  1. 1.Univ. Lille, CNRS, UMR 8524-Laboratoire Paul PainlevéLilleFrance
  2. 2.Department of Mathematics and Informatics“Lucian Blaga” University of SibiuSibiuRomania

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