On semigroups of nonnegative functions and positive operators

TL;DR

This paper extends results on nonnegative matrix semigroups to more general function semigroups, establishing conditions under which finiteness or boundedness can be deduced from local properties like linear functional values.

Contribution

It generalizes existing theorems from matrices to broader classes of functions, providing new criteria for semigroup boundedness and finiteness based on local properties.

Findings

Finiteness of nonnegative matrix semigroups can be deduced from local properties.

Boundedness criteria are extended to more general semigroups of functions.

Results connect linear functional values with global semigroup properties.

Abstract

We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals applied to them. We also consider more general semigroups of functions.