Riesz properties of a generalized Fredholm operator in a right quaternionic Hilbert space

Abstract

Newly, we have investigated and studied the basic properties of the class
of generalized Fredholm operators in a right quaternionic separable Hilbert space with   a left multiplication defined on it. In the present paper, we continue this study by   introducing another class of operators named the Riesz ones, which plays an important   role in this paper. More explicitly, we prove some important results on this class    of operators and we derive some Riesz properties of a generalized Fredholm operator    in this setting. The obtained results allow us to establish the relationship between    the Fredholm S-spectrum of a generalized Fredholm operator and the Fredholm Sspectrum
of it's generalized inverse, in a right quaternionic separable Hilbert space.