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http://dx.doi.org/10.4134/JKMS.j190439

PROPERTIES OF OPERATOR MATRICES  

An, Il Ju (Department of Applied Mathematics Kyung Hee University)
Ko, Eungil (Department of Mathematics Ewha Womans University)
Lee, Ji Eun (Department of Mathematics and Statistics Sejong University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 893-913 More about this Journal
Abstract
Let 𝓢 be the collection of the operator matrices $\(\array{A&C\\Z&B}\)$ 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.
Keywords
$2{\times}2$ operator matrices; the property (${\beta}$); decomposable; the property (C); Browder essential approximate point spectrum; Weyl's theorem; a-Weyl's theorem; a-Browder's theore;
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