On rank-one perturbations of normal operators

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

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

This paper is concerned with operators on Hilbert space of the form T = D + u ⊗ v where D is a diagonalizable normal operator and u ⊗ v is a rank-one operator. It is shown that if T ∉ C 1 and the vectors u and v have Fourier coefficients {αn}n = 1 and {βn}n = 1 with respect to an orthonormal basis that diagonalizes D that satisfy ∑n = 1 (| αn |2 / 3 + | βn |2 / 3) < ∞, then T has a nontrivial hyperinvariant subspace. This partially answers an open question of at least 30 years duration.

Original languageEnglish
Pages (from-to)628-646
Number of pages19
JournalJournal of Functional Analysis
Volume253
Issue number2
DOIs
StatePublished - 15 Dec 2007

Keywords

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

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