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arXiv · 1810.04199

Inverse continuity of the numerical range map for Hilbert space operators

Brian Lins·Ilya Spitkovsky
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Abstract

We describe continuity properties of the multivalued inverse of the numerical range map $f_A:x \mapsto \left\langle Ax, x \right\rangle$ associated with a linear operator $A$ defined on a complex Hilbert space $\mathcal{H}$. We prove in particular that $f_A^{-1}$ is strongly continuous at all points of the interior of the numerical range $W(A)$. We give examples where strong and weak continuity fail on the boundary and address special cases such as normal and compact operators.

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Brian Lins, Ilya Spitkovsky. 2018-10-09. Inverse continuity of the numerical range map for Hilbert space operators. https://arxiv.org/abs/1810.04199

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