On the weighted pseudo Drazin invertible elements in associative rings and Banach algebras


Jianlong Chen, Xiaofeng Chen, Hassane Zguitti




In this paper, we introduce and investigate the weighted pseudo Drazin inverse of elements in associative rings and Banach algebras. Some equivalent conditions for the existence of the w-pseudo Drazin inverse of a + b are given. Using the Pierce decomposition, the representations for the w-pseudo Drazin inverse are given in Banach algebras