Original scientific paper

https://doi.org/10.3336/gm.55.2.07

Further results on common properties of the products \(ac\) and \(bd\)

Qingping Zeng ; College of Computer and Information Sciences, Institute of Applied Mathematics, Fujian Agriculture and Forestry University, 350002 Fuzhou, P.R. China
Kai Yan ; College of Mathematics and Computer Science, Fuzhou University, 350108 Fuzhou, P.R. China
Zhenying Wu ; College of Mathematics and Informatics, Fujian Normal University, 350117 Fuzhou, P.R. China

Abstract

In this paper, we continue to investigate common properties of the products \(ac\) and $bd$ in various categories under the assumption $acd=dbd$ and $dba=aca$. These properties include generalized strongly Drazin invertibility and generalized Hirano invertibility in rings, abstract index of Fredholm elements and B-Fredholm elements in the Banach algebra context, complementability of kernels and ranges for bounded linear operators on Banach spaces.

Keywords

Jacobson's lemma; generalized inverse; complementability; index

Hrčak ID:

248667

URI

https://hrcak.srce.hr/248667

Publication date:

23.12.2020.

Visits: 1.131 *