On Koliha-Drazin invertible operators and Browder type theorems

On Koliha-Drazin invertible operators and Browder type theorems

Let $T$ be a bounded linear operator on a Banach space $X$. We give new necessary and sufficient conditions for $T$ to be Drazin or Koliha-Drazin invertible. All those conditions have the following form: $T$ possesses certain decomposition property and zero is not an interior point of some part of t...

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Bibliographic Details
Main Authors: Cvetković, Miloš D, Živković-Zlatanović, Snežana Č
Format: Journal Article
Language:English
Published: 01-12-2019
Subjects:
Mathematics - Functional Analysis
Online Access:Get full text
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Summary:Let $T$ be a bounded linear operator on a Banach space $X$. We give new necessary and sufficient conditions for $T$ to be Drazin or Koliha-Drazin invertible. All those conditions have the following form: $T$ possesses certain decomposition property and zero is not an interior point of some part of the spectrum of $T$. In addition, we study operators $T$ satisfying Browder\textquoteright s theorem, or a-Browder\textquoteright s theorem, by means of some relationships between diferent parts of the spectrum of $T$.
DOI:10.48550/arxiv.1912.00435