Characterization of the essential approximation S-spectrum and the essential defect S-spectrum in a right quaternionic Hilbert space

Abstract

In this paper, we introduce and study the essential approximation S-spectrum and the essential defect S-spectrum in the right quaternionic Hilbert space. Our results are used to describe the the investigation of the stability of the essential approximation S-spectrum and the essential defect S-spectrum of linear operator $A$ subjected to additive perturbation
$K$ such that $(2AK+K^2-2Re(\mathbf{q})K)R_\mathbf{q}(A+K)^{-1}$ or $R_\mathbf{q}(A+K)^{-1}(2AK+K^2-2Re(\mathbf{q})K)$ is a quasi-compact operator in the right quaternionic Hilbert space.