Generalized Drazin-Riesz invertible elements in a semi-simple Banach algebra
Othman Abad, Hassan Zguitti
TL;DR
This paper extends the concept of generalized Drazin-Riesz invertibility from bounded linear operators to elements in semi-simple Banach algebras, providing new characterizations and properties.
Contribution
It introduces the generalized Drazin-Riesz inverse in semi-simple Banach algebras and extends existing properties and characterizations from operator theory.
Findings
Extended the notion of generalized Drazin-Riesz inverse to Banach algebra elements.
Provided new characterizations of generalized Drazin-Riesz invertible elements.
Extended properties of these elements from operator theory to algebraic structures.
Abstract
We extend the notion of generalized Drazin-Riesz inverse introduced for bounded linear operators in \cite{Ziv} to elements in a complex unital semi-simple Banach algebra. Several characterizations and properties of generalized Drazin-Riesz invertible elements are given. In particular, we extend those of \cite{AbZg1,Djor,Ziv}.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMatrix Theory and Algorithms · Holomorphic and Operator Theory · Advanced Topics in Algebra