ON THE JOINT ESSENTIAL MAXIMAL NUMERICAL RANGES - CYPRIAN, O. S.; MASIBAYI, ANDREW; OKELO, N. B. (IJRDO -JOURNAL OF MATHEMATICS, 2015)
The concept of maximal numerical range of a bounded operator T on B(X) was introducedand studied in by Stampfli who used it to derive an identity for the norm of derivation. Thisconcept was later generalised by Ghan to the Joint maximal numerical range, , ofan m-tuple of operator . In 1997, Fong introduced the essentialmaximal numerical range to study the norm of a derivation on Calkin algebra. The Jointessential maximal numerical range was studied by Khan and certain results analogous to thesingle operator case proved. Khan also illustrated that the joint essential maximal numericalrange can be empty. In the present paper, we show the equivalent definitions of the jointessential maximal numerical range and also show that the Joint essentialmaximal numerical range is nonempty, compact and convex. We also show that each elementin the joint essential maximal numerical range is a star center of the joint maximal numericalrange.