On Numerical Ranges of Some Operators in Hilbert Spaces

Abstract

In this project, we investigate the numerical ranges of some basic operators. We develop the study of the Numerical ranges of these operators from the study of the resolvent sets, the spectrum(the classical classification of the spectrum) and the numerical radii of some of these operators under study. We then cap it off by an insightful look at the Numerical ranges of some selected operators. We will also get to study pseudo-spectrum and essential spectrum as part of the wider classification of the spectrum of some operators.