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
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