Geodesic
Operator matrices and their Weyl type theorems
Filomat, Tome 34 (2020) no. 10, p. 3191

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DOI

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.
DOI : 10.2298/FIL2010191A
Classification : 47A10, 47A53, 58B15
Keywords: 2 × 2 operator matrices, Browder essential approximate point spectrum, generalized Weyl’s theorem, generalized a-Weyl’s theorem, generalized a-Browder’s theorem 
Il Ju An; Eungil Ko; Ji Eun Lee. Operator matrices and their Weyl type theorems. Filomat, Tome 34 (2020) no. 10, p. 3191 . doi: 10.2298/FIL2010191A
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     author = {Il Ju An and Eungil Ko and Ji Eun Lee},
     title = {Operator matrices and their {Weyl} type theorems},
     journal = {Filomat},
     pages = {3191 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010191A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010191A/}
}
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