Riesz Projection and Essential S-spectrum in Quaternionic Setting

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 Sresolvent operators. Inspired by the S-resolvent equation, we give the Browder's S-resolvent equation in quaternionic setting. Contents 1. Introduction 1 2. Mathematical preliminaries 4 2.1. Quaternions 4 2.2. Operators acting on right quaternionic Hilbert space 5 2.3. The quaternionic functional calculus 6 3. Eigenvalue of finite type 9 4. Browder S-resolvent equation in quaternionic setting 17 References 22