On rank-one perturbations of normal operators, II

C. Foias, I. B. Jung, E. Ko, C. Pearcy

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

AS the title indicates, this note is a sequel to [2], in which we showed that a large class of rank-one perturbations of a diagonalizable normal operator have nontrivial hyperinvariant subspaces. Below we establish the perhaps surprising fact that the commutants of such operators are abelian, paralleling thereby the properties of the commutants of normal operators of multiplicity one. We also show by example that this behavior does not extend to the commutants of rank-one perturbations of all normal operators of multiplicity one, and we discuss similarity and quasisimilarity questions associated with this class of operators.

Original languageEnglish
Pages (from-to)2745-2760
Number of pages16
JournalIndiana University Mathematics Journal
Volume57
Issue number6
DOIs
StatePublished - 2008

Keywords

  • Hyperinvariant subspace
  • Invariant subspace
  • Normal operator
  • Quasisimilarity
  • Rank-one perturbation
  • Similarity

Fingerprint

Dive into the research topics of 'On rank-one perturbations of normal operators, II'. Together they form a unique fingerprint.

Cite this