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arXiv · 2003.05347

Numerical ranges encircled by analytic curves

Brian Lins
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Abstract

Let $D$ be a bounded convex domain in $\mathbb{C}$ with a regular analytic boundary. Suppose that the numerical range $W(A)$ of a bounded linear operator $A$ is contained in $\overline{D}$. If $\overline{W(A)}$ intersects the boundary $\partial D$ at infinitely many points while the essential numerical range $W_\text{ess}(A)$ does not intersect $\partial D$, then $W(A) = \overline{D}$. This generalizes some infinite dimensional analogues of a result of Anderson.

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Brian Lins. 2020-03-11. Numerical ranges encircled by analytic curves. https://arxiv.org/abs/2003.05347

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