Abstract:
For bounded right linear operators, in a right quaternionic Hilbert space with a left
multiplication defined on it, we study the approximate S-point spectrum. In the same
Hilbert space, then we study the Fredholm operators and the Fredholm index. In par ticular, we prove the invariance of the Fredholm index under small norm operator and
compact operator perturbations. Finally, in association with the Fredholm operators,
we develop the theory of essential S-spectrum. We also characterize the S-spectrum
in terms of the essential S-spectrum and Fredholm operators. In the sequel, we study
left and right S-spectra as needed for the development of the theory presented in this
note. Published by AIP Publishing. https://doi.org/10.1063/1.5040017
