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arxiv: 1702.00668 · v1 · pith:7IT6STEUnew · submitted 2017-02-02 · 🧮 math.FA

The numerical range as a spectral set

Michel Crouzeix , C\'esar Palencia This is my paper
classification 🧮 math.FA
keywords numericaloperatorrangespectralbehaviorcauchycompleteconjugates
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It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of holomorphic functions.

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