Pseudo S-spectrum in a right quaternionic Hilbert space

The issue of the S-spectrum introduced by Colombo et al. [Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions. Basel: Birkhauser/Springer Basel AG; 2011. (Progress in mathematics; vol. 289). p. vi+221]. motivates us to investigate the pseudo S-spectrum of a bounded right quaternionic linear operator, in a right quaternionic Hilbert space with a left multiplication defined on it. Besides, we give a characterization for the Weyl pseudo S-spectrum in terms of the Fredholm operators with the aid of results from the papers [Muraleetharan, Thirulogasanthar. Fredholm operators and essential S-spectrum in the quaternionic setting. J Math Phys. 2018;59(10):103506, 27 pp.; Muraleetharan, Thirulogasanthar. Weyl and Browder S-spectra in a right quaternionic Hilbert space. J Geom Phys. 2019;135:7-20].