Generalizations of the relation of quasisimilarity for operators

H. Bercovici, I. B. Jung, E. Ko, C. Pearcy

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Abstract

In this note we first briefly review the progress on the hyperinvari-ant subspace problem for operators on Hilbert space made possible by the equivalence relation of ampliation quasisimilarity recently introduced in [7]. Then we introduce another equivalence relation, which we call pluquasisimilarity , with bigger equivalence classes than ampliation quasisimilarity but very different in appearance, which preserves the existence of hyperinvariant sub-spaces for operators, and thus may be useful in the future. We also compare these with two other equivalence relations, injection-similarity and complete injection-similarity, introduced long ago by Sz.-Nagy and Foias in [13].

Original languageEnglish
Pages (from-to)681-691
Number of pages11
JournalActa Scientiarum Mathematicarum
Volume85
Issue number3-4
DOIs
StatePublished - 2019

Keywords

  • Ampliation quasisimilarity
  • Hyperinvariant subspace
  • Quasi-affinity
  • Quasisimilarity
  • Quasitriangular operator

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