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A note on the generalized Drazin–Riesz invertible operators

A note on the generalized Drazin–Riesz invertible operators We study generalized Drazin–Riesz invertible operators. Among other things, we show that if a bounded linear operator T is generalized Drazin–Riesz invertible then its generalized Drazin–Riesz inverse may be not unique. We also show that generalized Drazin–Riesz invertible operators are stable under commuting perturbation by Riesz operators. Applications to the abstract singular differential equations are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Functional Analysis Springer Journals

A note on the generalized Drazin–Riesz invertible operators

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Publisher
Springer Journals
Copyright
Copyright © Tusi Mathematical Research Group (TMRG) 2021
ISSN
2639-7390
eISSN
2008-8752
DOI
10.1007/s43034-021-00142-9
Publisher site
See Article on Publisher Site

Abstract

We study generalized Drazin–Riesz invertible operators. Among other things, we show that if a bounded linear operator T is generalized Drazin–Riesz invertible then its generalized Drazin–Riesz inverse may be not unique. We also show that generalized Drazin–Riesz invertible operators are stable under commuting perturbation by Riesz operators. Applications to the abstract singular differential equations are given.

Journal

Annals of Functional AnalysisSpringer Journals

Published: Oct 1, 2021

Keywords: Drazin invertible operator; Riesz operator; Browder operator; 47A10; 47A53; 47A55; 47A25

References