# A note on the spectrum of irreducible operators and semigroups

@inproceedings{Gluck2021ANO, title={A note on the spectrum of irreducible operators and semigroups}, author={Jochen Gluck}, year={2021} }

Let $T$ denote a positive operator with spectral radius $1$ on, say, an $L^p$-space. A classical result in infinite dimensional Perron--Frobenius theory says that, if $T$ is irreducible and power bounded, then its peripheral point spectrum is either empty or a subgroup of the unit circle.
In this note we show that the analogous assertion for the entire peripheral spectrum fails. More precisely, for every finite union $U$ of finite subgroups of the unit circle we construct an irreducible…

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