Collective order boundedness of sets of operators between ordered vector spaces

It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given.