## Taiwanese Journal of Mathematics

### STRONGLY CONTINUOUS GROUPS, SIMILARITY AND NUMERICAL RANGE ON A HILBERT SPACE

Ralph deLaubenfels

#### 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 $\{z \in {\bf C} \, | \, |Im(z)| \lt \alpha \}$.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 2 (1997), 127-133.

Dates
First available in Project Euclid: 18 July 2017