Properties of operator matrices

Il Ju An, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let S be the collection of the operator matrices (AZ BC) where the range of C is closed. In this paper, we study the properties of operator matrices in the class S. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class S and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class S, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl’s theorem and a-Browder’s theorem, respectively.

Original languageEnglish
Pages (from-to)893-913
Number of pages21
JournalJournal of the Korean Mathematical Society
Volume57
Issue number4
DOIs
StatePublished - 2020

Keywords

  • 2 × 2 operator matrices
  • A-Browder’s theorem
  • A-Weyl’s theorem
  • Browder essential approximate point spectrum
  • Decomposable
  • The property (C)
  • The property (β)
  • Weyl’s theorem

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