Non commutative functional calculus: bounded operators

TL;DR

This paper introduces a new functional calculus for bounded operators on quaternionic Banach spaces, utilizing slice-regularity, a novel resolvent operator, and an eigenvalue problem to extend operator analysis in non-commutative settings.

Contribution

It develops a new functional calculus framework for quaternionic operators based on slice-regularity, including innovative resolvent and eigenvalue concepts.

Findings

Established a new resolvent operator for quaternionic operators

Formulated a novel eigenvalue problem in quaternionic Banach spaces

Extended functional calculus to non-commutative quaternionic operators

Abstract

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see \cite{gs}, and the key tools are a new resolvent operator and a new eigenvalue problem.