Remarks on the crouzeix-Palencia proof that the numerical range is a (1 +√2)-spectral set

Thomas Ransford; Felix L. Schwenninger

doi:10.1137/17M1143757

Remarks on the crouzeix-Palencia proof that the numerical range is a (1 +√2)-spectral set

Thomas Ransford, Felix L. Schwenninger

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Abstract

Crouzeix and Palencia recently showed that the numerical range of a Hilbert-space operator is a (1 + √2)-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 + √2) is sharp.

Original language	English
Pages (from-to)	342-345
Number of pages	4
Journal	SIAM journal on matrix analysis and applications
Volume	39
Issue number	1
DOIs	https://doi.org/10.1137/17M1143757
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Cauchy transform
Crouzeix's conjecture
Numerical range
Spectral set

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Ransford2018remarksFinal published version, 257 KBLicence: CC BY-NC

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Remarks on the crouzeix-Palencia proof that the numerical range is a (1 +√2)-spectral set

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