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arXiv · 2005.10136

A new approach to the S-functional calculus

El Hassan Benabdi·Mohamed Barraa
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Abstract

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.

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El Hassan Benabdi, Mohamed Barraa. 2020-05-20. A new approach to the S-functional calculus. https://arxiv.org/abs/2005.10136

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