The numerical range as a spectral set

Michel Crouzeix; César Palencia

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arXiv · 1702.00668

The numerical range as a spectral set

Michel Crouzeix·César Palencia

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Abstract

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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Michel Crouzeix, César Palencia. 2017-02-02. The numerical range as a spectral set. https://arxiv.org/abs/1702.00668

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