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arXiv · 2105.13105

Drazin invertibility of linear operators on quaternionic Banach spaces

El Hassan Benabdi·Mohamed Barraa
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Abstract

Let $A$ be a right linear operator on a two-sided quaternionic Banach space $X$. The paper studies the Drazin inverse for right linear operators on a 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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El Hassan Benabdi, Mohamed Barraa. 2021-05-27. Drazin invertibility of linear operators on quaternionic Banach spaces. https://arxiv.org/abs/2105.13105

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