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

Jianlong Chen, Xiaofeng Chen, Hassane Zguitti

Abstract


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

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