Spectral decomposability of rank-one perturbations of normal operators

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

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10 Scopus citations

Abstract

This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoarǎ and Foias (1968) [1].

Original languageEnglish
Pages (from-to)602-609
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume375
Issue number2
DOIs
StatePublished - 15 Mar 2011

Keywords

  • Decomposable operator
  • Hyperinvariant subspace
  • Invariant subspace
  • Normal operator
  • Rank-one perturbation

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