Extending monotone seminorms on partially ordered vector spaces

Onno van Gaans
1998 Indagationes mathematicae  
Given a monotone seminorm on a directed partially ordered vector space, the question arises whether it can be extended to a monotone seminorm on the Dedekind completion. This paper presents a necessary condition and proves it to be sufficient for existence of a largest extension on any partially ordered vector space that contains the given space as a majorizing subspace. Furthermore, the aspects of uniqueness and norm completeness are studied.
doi:10.1016/s0019-3577(98)80003-7 fatcat:vaup57j4inbmph24rdrqn7aqry