Drazin invertibility of linear operators on quaternionic Banach spaces


  • El Hassan Benabdi Department of Mathematics, Laboratory of Mathematics, Statistics and Applications, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco
  • Mohamed Barraa Department of Mathematics, Faculty of Sciences Semlalia, University Cadi Ayyad, Marrakesh, Morocco




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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