On the joint essential maximal numerical ranges

Abstract

The concept of maximal numerical range of a bounded operator T on B(X) was introduced and studied in by Stampfli who used it to derive an identity for the norm of derivation. This concept was later generalised by Ghan to the Joint maximal numerical range..., , of an m-tuple of operator.... In 1997, Fong introduced the essential maximal numerical range to study the norm of a derivation on Calkin algebra. The Joint essential maximal numerical range was studied by Khan and certain results analogous to the single operator case proved. Khan also illustrated that the joint essential maximal numerical range can be empty. In the present paper, we show the equivalent definitions of the joint essential maximal numerical range...and also show that the Joint essential maximal numerical range is nonempty, compact and convex. We also show that each element in the joint essential maximal numerical range is a star center of the joint maximal numerical range.