Abstract
Maximal operator semigroups, bounded in a certain sense, on real or complex vector spaces are studied. For any maximal semigroup M dominated by a certain pair of homogeneous functions there is an operator quasinorm for which M is exactly the semigroup of contractions in this quasinorm. Applications to Riesz spaces are given. In particular, maximal semigroups of matrices dominated by a given positive matrix are characterized. We thus answer the question implicitly posed in [2].
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