English

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 T=iTiT=\bigoplus_i T_i in terms of the numerical ranges {W(Ti)}i\{W(T_i)\}_i of its components. Specifically, the essential numerical range of TT is the convex hull of the limit superior of {W(Ti)}i\{W(T_i)\}_i. This characterization can be simplified further. In fact, we prove the existence of a decomposition of TT 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}
}
R2 v1 2026-06-28T07:48:40.194Z