Representations for the pseudo Drazin inverse of elements in a Banach algebra - Zhu, Huihui (2015)
In this paper, we investigate the pseudo Drazin invertibility of the sum and the product of elements in a Banach algebra A. Given pseudo Drazin invertible elements a and b such that a2b=aba and b2a=bab, it is shown that ab is pseudo Drazin invertible and a+b is pseudo Drazin invertible if and only if so is 1+a^\ddag b, and the related formulae are provided.