Glasnik Matematicki, Vol. 55, No. 2 (2020), 267-276.

FURTHER RESULTS ON COMMON PROPERTIES OF THE PRODUCTS AC AND BD

Qingping Zeng, Kai Yan and Zhenying Wu

College of Computer and Information Sciences, Institute of Applied Mathematics, Fujian Agriculture and Forestry University, 350002 Fuzhou, P.R. China
e-mail: zqpping2003@163.com

College of Mathematics and Computer Science, Fuzhou University, 350108 Fuzhou, P.R. China
e-mail: yklolxj@163.com

College of Mathematics and Informatics, Fujian Normal University, 350117 Fuzhou, P.R. China
e-mail: zhenyingwu2011@163.com

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.

2010 Mathematics Subject Classification.   15A09, 16U99, 47A05, 47A53

Key words and phrases.   Jacobson's lemma, generalized inverse, complementability, index

Full text (PDF) (free access)

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

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