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arXiv · 1804.04062

Spectral sets and operator radii

Catalin Badea·Michel Crouzeix·Hubert Klaja
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Abstract

We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set for a Hilbert space operator, then it is a $M$-numerical radius set, where $M=\frac{1}{2}(K+K^{-1})$. This is a counterpart of a recent result of Davidson, Paulsen and Woerdeman. More general results for operator radii associated with the class of operators having $\rho$-dilations in the sense of Sz.-Nagy and Foias are given. A version of a result of Drury concerning the joint numerical radius of non-commuting $n$-tuples of operators is also obtained.

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Catalin Badea, Michel Crouzeix, Hubert Klaja. 2018-04-11. Spectral sets and operator radii. https://doi.org/10.1112/blms.12191

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