Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set

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.

Locations

• SIAM Journal on Matrix Analysis and Applications - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View