A theoretical investigation of S-Numerical Range with the respect to a family of projections

Abstract

The idea of the -numerical range of a bounded linear operator on a complex Hilbert space with respect to a family of projections is introduced in this study. We provide a detailed description and discuss its relationship to the -numerical range and generalizations such as product S-numerical range. The significance of this new concept comes from its unifying character.

Keywords

• S-numerical range, projections, spectrum, bounded operator