Open AccessOperator matrices and their Weyl type theorems
Author(s) -
Ilsin An,
Eungil Ko,
Ji Eun Lee
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2010191a
Subject(s) - mathematics , operator (biology) , spectrum (functional analysis) , pure mathematics , type (biology) , matrix (chemical analysis) , algebra over a field , simple (philosophy) , biochemistry , ecology , chemistry , physics , materials science , philosophy , epistemology , repressor , quantum mechanics , biology , transcription factor , composite material , gene
We denote the collection of the 2 x 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.