Domination properties and extension of positive compact operators on pre-Riesz spaces

Abstract

This paper concerns positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space to the Riesz completion. It extends the order continuous norms in pre-Riesz spaces to Riesz completions. The compactness of third power of a positive operator is obtained in a pre-Riesz space which has an order unit.