On a generalized q-numerical Range

Abstract

We 'consider numerical ranges of a bounded linear operator on complex Hilbert spaces. Many properties of the classical numerical range are known. We investigate the properties of the q-numerical range in relation to those of the classical numerical range. We also establish the relationship between the q-numerical range and the algebra q-numerical range. Furthermore, we extend the results of the classical numerical range and q-numerical range to the C-numerical range and investigate how the C-numerical range is an explicit generalization of both the classical numerical range and q-numerical range.