The quasi-similarity and dominant conditions of Weyl spectrum in a complex Hilbert space

Abstract

The study of spectrum in Hilbert spaces is a very rich in giving more structures of the spectrum and we wish to go in to depth to understand deeper on the structure of the spectrum. Apart from the well-known components of spectrum i.e. spectrum, the approximate point spectrum, the point spectrum and the set of eigenvalues of finite multiplicity: there is need for further study on the Weyl spectrum of an Operator in a complex Hilbert space. To succeed in this study, two conditions to help expose properties of the Weyl spectrum i.e. Quasi-Similarity and the dominant condition will be used.