Weyl and Browder S-spectrums in a right quaternionic Hilbert space

TL;DR

This paper investigates the Weyl and Browder S-spectrums of bounded right quaternionic linear operators in quaternionic Hilbert spaces, providing characterizations and introducing new spectral concepts.

Contribution

It introduces the Browder S-spectrum and characterizes the S-spectrum via Weyl operators in the quaternionic setting, extending spectral theory.

Findings

Characterization of the S-spectrum using Weyl operators

Introduction of the Browder S-spectrum in quaternionic Hilbert spaces

Analysis of properties of Weyl and Browder operators in this context

Abstract

In this note first we study the Weyl operators and Weyl S-spectrum of a bounded right quaternionic linear operator, in the setting of the so-called S-spectrum, in a right quaternionic Hilbert space. In particular, we give a characterization for the S-spectrum in terms of the Weyl operators. In the same space we also study the Browder operators and introduce the Browder S-spectrum.