On Numerical and Centre Values Range

Abstract

This paper follows [1] in the quantitative study of Numerical Ranges introduced by Stampfli [9]. In particular, we consider a family of mutually orthogonal projections and investigate how a numerical range can be related to several other numerical ranges in a closed convex hull. We then introduce the centre valued range and show that if U is a W∗- algebra then for any A in U we can relate the norm of A and distance of A itself from its centre.