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arXiv · 2212.11659

A note on the essential numerical range of block diagonal operators

Luís Carvalho·Cristina Diogo·Sérgio Mendes·Helena Soares
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Abstract

In this note we characterize the essential numerical range of a block diagonal o\-pe\-ra\-tor $T=\bigoplus_i T_i$ in terms of the numerical ranges $\{W(T_i)\}_i$ of its components. Specifically, the essential numerical range of $T$ is the convex hull of the limit superior of $\{W(T_i)\}_i$. 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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Luís Carvalho, Cristina Diogo, Sérgio Mendes, Helena Soares. 2022-12-22. A note on the essential numerical range of block diagonal operators. https://arxiv.org/abs/2212.11659

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