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

Thomas Ransford, Felix L. Schwenninger

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
4 Downloads (Pure)

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 languageEnglish
Pages (from-to)342-345
Number of pages4
JournalSIAM journal on matrix analysis and applications
Volume39
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes

Keywords

  • Cauchy transform
  • Crouzeix's conjecture
  • Numerical range
  • Spectral set

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