Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.06.26
  • Accepted : 2020.03.25
  • Published : 2020.07.01
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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

Acknowledgement

The first author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(2017R1C1B1006538). The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(2019R1F1A1058633). The third author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2019R1A2C1002653).

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