Hubert Klaja, Javad Mashreghi, Thomas Ransford
Published 2017-01-19Version 1
We define and study a numerical-range analogue of the notion of spectral set. Among the results obtained are a positivity criterion and a dilation theorem, analogous to those already known for spectral sets. An important difference from the classical definition is the role played in the new definition by the base point. We present some examples to illustrate this aspect.
The numerical range as a spectral set
Remarks on the Crouzeix-Palencia proof that the numerical range is a $(1+\sqrt2)$-spectral set
The possible shapes of numerical ranges
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