On local spectral properties of operator matrices

Il Ju An, Eungil Ko, Ji Eun Lee

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In this paper, we focus on a 2 × 2 operator matrix Tϵk as follows: Tϵk=(ACϵkDB), where ϵk is a positive sequence such that lim kϵk= 0. We first explore how Tϵk has several local spectral properties such as the single-valued extension property, the property (β) , and decomposable. We next study the relationship between some spectra of Tϵk and spectra of its diagonal entries, and find some hypotheses by which Tϵk satisfies Weyl’s theorem and a-Weyl’s theorem. Finally, we give some conditions that such an operator matrix Tϵk has a nontrivial hyperinvariant subspace.

Original languageEnglish
Article number164
JournalJournal of Inequalities and Applications
Issue number1
StatePublished - 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).


  • 2 × 2 operator matrices
  • Decomposable
  • Hyperinvariant subspace
  • The property (β)
  • The single-valued extension property
  • Weyl’s theorem


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