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 |
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Pages (from-to) | 342-345 |
Number of pages | 4 |
Journal | SIAM journal on matrix analysis and applications |
Volume | 39 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Externally published | Yes |
Keywords
- Cauchy transform
- Crouzeix's conjecture
- Numerical range
- Spectral set