A note on the essential numerical range of block diagonal operators
Functional Analysis
2022-12-23 v1
Abstract
In this note we characterize the essential numerical range of a block diagonal o\-pe\-ra\-tor in terms of the numerical ranges of its components. Specifically, the essential numerical range of is the convex hull of the limit superior of . This characterization can be simplified further. In fact, we prove the existence of a decomposition of for which the convex hull is not required.
Keywords
Cite
@article{arxiv.2212.11659,
title = {A note on the essential numerical range of block diagonal operators},
author = {Luís Carvalho and Cristina Diogo and Sérgio Mendes and Helena Soares},
journal= {arXiv preprint arXiv:2212.11659},
year = {2022}
}