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 language | English |
|---|---|
| Pages (from-to) | 893-913 |
| Number of pages | 21 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:Received June 26, 2019; Revised December 12, 2019; Accepted March 25, 2020. 2010 Mathematics Subject Classification. Primary 47A53, 47A55, 47A10, 47B40. Key words and phrases. 2 × 2 operator matrices, the property (β), decomposable, the property (C), Browder essential approximate point spectrum, Weyl’s theorem, a-Weyl’s theorem, a-Browder’s theorem. 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).
Publisher Copyright:
© 2020 Korean Mathematial Soiety.
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