Maximal dominated operator semigroups

Maksimal operator semigroups, bounded in a certain sense, on real or complex vector spaces are studied. Let X be a vector space with dual space X'. Denote by a nonzero subspace of X' and let n : X [0, ), n' : [0, ) be given homogeneous functions. It is studied collections C of operators on X such that each operator T C is dominated by the pair (n, n'), i.e., ( ) ( Tx n )n(x) ' for all xX and all . One of the results proved in this work is that for any maximal semigroup M of operators dominated by such a pair of homogeneous functions there exists an operator quasi-norm for which M = {T L(X) : T 1}. Applications of these general results are then given to maximal semigroups of regular operators on a Riesz space dominated by a fixed positive linear operator. In particular, maximal semigroups of matrices dominated by a given positive matrix are characterized. Keywords: Operators, vector spaces, semigroups, contractions, domination, Riesz spaces