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arXiv · 1708.08633

Remarks on the Crouzeix-Palencia proof that the numerical range is a $(1+\sqrt2)$-spectral set

Thomas Ransford·Felix Schwenninger
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Abstract

Crouzeix and Palencia recently showed that the numerical range of a Hilbert-space operator is a $(1+\sqrt2)$-spectral set for the operator. One of the principal ingredients of their proof can be formulated as an abstract functional-analysis lemma. We give a new short proof of the lemma and show that, in the context of this lemma, the constant $(1+\sqrt2)$ is sharp.

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Thomas Ransford, Felix Schwenninger. 2017-08-29. Remarks on the Crouzeix-Palencia proof that the numerical range is a $(1+\sqrt2)$-spectral set. https://doi.org/10.1137/17m1143757

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