2014•FilomatOpen access

Additive property of pseudo Drazin inverse of elements in Banach algebras

Huihui Zhu, Jianlong Chen

Abstract

This article concerns the pseudo Drazin inverse of the sums (resp. differences) and the products of elements in a Banach algebra A. Some equivalent conditions for the existence of the pseudo Drazin inverse of a + b (resp. a - b) are characterized. Moreover, the representations for the pseudo Drazin inverse are given. Some related known results are generalized.

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Key concepts: Drazin inverse, Mathematics, Banach algebra, Inverse, Pure mathematics, Property (philosophy), Banach space, Algebra over a field