Fredholm operators and essential S-spectrum in the quaternionic setting

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 particular, we prove the invariance of the Fredholm index under small norm operator and compact operator perturbations. Finally, in association with 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-spectrums as needed for the development of the theory presented in this note.

29 pages

References in corpus (6)

• Continuous slice functional calculus in quaternionic Hilbert spaces
• Non commutative functional calculus: unbounded operators
• Non commutative functional calculus: bounded operators
• Dirac solutions for quaternionic potentials
• Coherent state Quantization of quaternions
• Deficiency Indices of Some Classes of Unbounded $\mathbb{H}$-Operators

Cited by in corpus (6)

• Weyl and Browder S-spectrums in a right quaternionic Hilbert space
• Kato S-spectrum in the quaternionic setting
• Perturbation of Continuous Frames on Quaternionic Hilbert Spaces
• Decomposable operators, local S-spectrum and S-spectrum in the quaternionic setting
• Berberian extension and its S-spectra in a quaternionic Hilbert space
• Universality property of the $S$-functional calculus, noncommuting matrix variables and Clifford operators