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


Aymen Ammar, Aref Jeribi, Bilel Saadaoui




In this paper, we introduce and study the essential approximation S-spectrum and the essential defect S-spectrum in a right quaternionic Hilbert space. Our results are used to describe 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 (AK + KA + K 2 − 2Re(q)K)R q (A + K) −1 or R q (A + K) −1 (AK + KA + K 2 − 2Re(q)K) is a quasi-compact operator in the right quaternionic Hilbert space.