Further results on common properties of the products ac and bd - Zeng, Qingping (Array, 2020)
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.