Abstract
It is shown that $iB$ generates a strongly continuous group of exponential type $\omega$ on a Hilbert space if and only if for all $\alpha \gt \omega$, $B$ is similar to an operator with spectrum and numerical range contained in the horizontal strip $\{z \in {\bf C} \, | \, |Im(z)| \lt \alpha \}$.
Citation
Ralph deLaubenfels. "STRONGLY CONTINUOUS GROUPS, SIMILARITY AND NUMERICAL RANGE ON A HILBERT SPACE." Taiwanese J. Math. 1 (2) 127 - 133, 1997. https://doi.org/10.11650/twjm/1500405229
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