A note on the essential numerical range of block diagonal operators
Abstract
In this note we characterize the essential numerical range of a block diagonal o\-pe\-ra\-tor T=i Ti in terms of the numerical ranges \W(Ti)\i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of \W(Ti)\i. This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.
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