Hyperinvariant subspaces for a class of quasinilpotent operators

Il Bong Jung, Eungil Ko, Carl Pearcy

Research output: Contribution to journalArticlepeer-review


Quasinilpotent operators on Hilbert space are very little understood. Except for the classification, up to similarity, as parts of quasinilpotent backward weighted shifts of infinite multiplicity (Foiaş and Pearcy, 1974), and the recently introduced technique of extremal vectors (see the references), there are few known structure theorems or theorems proving the existence of invariant or hyperinvariant subspaces for such operators. In this paper we use a structure theorem for the class of weakly centered operators (Paulsen et al., 1995) to obtain a structure theorem for a certain subclass of quasinilpotent operators that immediately yields the existence of hyperinvariant subspaces for such operators.

Original languageEnglish
Pages (from-to)289-296
Number of pages8
JournalStudia Mathematica
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 Instytut Matematyczny PAN.


  • Centered operator
  • Hyperinvariant subsace
  • Invariant subspace
  • Quasinilpotent operator
  • Weakly centered operator


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