Browder S-resolvent equation in quaternionic setting

TL;DR

This paper extends the S-resolvent equation to quaternionic operators, exploring S-eigenvalues, Riesz projections, and Browder's S-resolvent equation in quaternionic Hilbert spaces.

Contribution

It introduces the Browder S-resolvent equation in the quaternionic setting, advancing the spectral theory of quaternionic linear operators.

Findings

Defined S-eigenvalues of finite type in quaternionic operators

Established properties of Riesz projections in quaternionic context

Derived Browder's S-resolvent equation for quaternionic operators

Abstract

This paper is devoted to the study of the S-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S-spectrum. Furthermore, we introduce the left and right Browder S-resolvent operators. Inspired by the S-resolvent equation, we give the Browder's S-resolvent equation in quaternionic setting.