Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3191-3204 |
| Number of pages | 14 |
| Journal | Filomat |
| Volume | 34 |
| Issue number | 10 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:2010 Mathematics Subject Classification. Primary 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 Received: 11 October 2019; Accepted:11 February 2020 Communicated by Dragan S. Djordjević Corresponding author: Ji Eun Lee The first author was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Science and ICT(NRF-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 the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(2019R1A2C1002653). Email addresses: 66431004@naver.com (Il Ju An), eiko@ewha.ac.kr (Eungil Ko), jieunlee7@sejong.ac.kr; jieun7@ewhain.net (Ji Eun Lee)
Publisher Copyright:
© 2020, University of Nis. All rights reserved.
Keywords
- 2 × 2 operator matrices
- Browder essential approximate point spectrum
- Generalized a-browder’s theorem
- Generalized a-weyl’s theorem
- Generalized weyl’s theorem