Jeribi essential and Jeribi essential pseudo S-spectra in right quaternionic Hilbert space

In this note, we extend our exploration of the essential S-spectrum and introduce the class of Jeribi essential pseudo S-spectrum for bounded right linear operators over the right quaternionic Hilbert space. We explore several properties and the stability of the essential S-spectrum and essential pseudo S-spectrum of this class. Furthermore, we study relationships between the Jeribi essential S-spectrum and other essential S-spectra while investigating the correlation of the essential S-spectrum of this class for 2 × 2 block operator matrices with their components and formulating a characterization of the Jeribi essential S-spectrum for the summation of two bounded linear operators. The study concludes by introducing the notion of essential pseudo S-spectrum of this class and exploration of some of the algebraic properties.