Operator matrices and their weyl type theorems

Il Ju An, Eungil Ko, Ji Eun Lee, Dragan S. Djordjević

Research output: Contribution to journalArticlepeer-review

Abstract

We denote the collection of the 2 × 2 operator matrices with (1, 2)-entries having closed range by S. In this paper, we study the relations between the operator matrices in the class S and their component operators in terms of the Drazin spectrum and left Drazin spectrum, respectively. As some application of them, we investigate how the generalized Weyl’s theorem and the generalized a-Weyl’s theorem hold for operator matrices in S, respectively. In addition, we provide a simple example about an operator matrix in S satisfying such Weyl type theorems.

Original languageEnglish
Pages (from-to)3191-3204
Number of pages14
JournalFilomat
Volume34
Issue number10
DOIs
StatePublished - 2020

Keywords

  • 2 × 2 operator matrices
  • Browder essential approximate point spectrum
  • Generalized a-browder’s theorem
  • Generalized a-weyl’s theorem
  • Generalized weyl’s theorem

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