A Note on Drazin Invertibility for Upper Triangular Block Operators |
| |
Authors: | Hassane Zguitti |
| |
Institution: | 1. Department of Mathematics and Computer Science, Multidisciplinary Faculty of Nador, University of Mohammed I, PO Box 300 Selouane, Nador, 62702, Morocco
|
| |
Abstract: | A bounded linear operator A acting on a Banach space X is said to be an upper triangular block operators of order n, and we write ${A \in \mathcal{UT}_{n}(X)}$ , if there exists a decomposition of ${X = X_{1} \oplus . . . \oplus X_{n}}$ and an n × n matrix operator ${(A_{i,j})_{\rm 1 \leq i, j \leq n}}$ such that ${A = (A_{i, j})_{1 \leq i, j \leq n}, A_{i, j} = 0}$ for i > j. In this note we characterize a large set of entries A i, j with j > i such that ${\sigma_{\rm D} (A) = {\bigcup\limits_{i = 1}^{n}} \sigma_{\rm D} (A_{i, i})}$ ; where σD(.) is the Drazin spectrum. Some applications concerning the Fredholm theory and meromorphic operators are given. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|