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Drazin invertibility of linear operators on quaternionic Banach spaces
El Hassan Benabdi and Mohamed Barraa

Volume 65, no. 2 (2023), pp. 277–284    

Published online: October 31, 2023

https://doi.org/10.33044/revuma.2700

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Abstract

The paper studies the Drazin inverse for right linear operators on a quaternionic Banach space. Let $A$ be a right linear operator on a two-sided quaternionic Banach space. It is shown that if $A$ is Drazin invertible then the Drazin inverse of $A$ is given by $f(A)$, where $f$ is $0$ in an axially symmetric neighborhood of $0$ and $f(q) = q^{-1}$ in an axially symmetric neighborhood of the nonzero spherical spectrum of $A$. Some results analogous to the ones concerning the Drazin inverse of operators on complex Banach spaces are proved in the quaternionic context.

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