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.
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