Michel Crouzeix, César Palencia
Published 2017-02-02Version 1
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.
The numerical range of a contraction with finite defect numbers
Multipliers on Hilbert spaces of functions on R
Frames of subspaces in Hilbert spaces with $W$-metrics
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