On the generalized Drazin inverse of the sum in a Banach algebra
Dijana Mosic, Daochang Zhang
TL;DR
This paper investigates conditions under which the sum of two elements in a Banach algebra has a generalized Drazin inverse, providing explicit formulas for such inverses under new assumptions.
Contribution
It introduces new conditions for the existence of the generalized Drazin inverse of a sum in a Banach algebra and derives explicit formulas for it.
Findings
Established new sufficient conditions for the existence of the generalized Drazin inverse of a sum.
Derived explicit formulas for the generalized Drazin inverse of the sum under these conditions.
Extended previous results by relaxing assumptions on the elements involved.
Abstract
The objective of this paper is to study the existence of the generalized Drazin inverse of the sum in a Banach algebra and present explicit expressions for the generalized Drazin inverse of this sum, under new conditions.
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 · Advanced Optimization Algorithms Research · Iterative Methods for Nonlinear Equations