In this paper, we first prove that the S-spectrum of a bounded right quaternionic linear operator on a two-sided quaternionic Banach space is a union of the spectrum of some bounded linear operators on a complex Banach space. Furthermore, we show that the S-functional calculus is obtained by the Riesz-Dunford functional calculus for complex linear operators. We also give simple proofs of some already existing results.
@article{arxiv.2005.10136,
title = {A new approach to the S-functional calculus},
author = {El Hassan Benabdi and Mohamed Barraa},
journal= {arXiv preprint arXiv:2005.10136},
year = {2020}
}