Characterizing Riesz* homomorphisms via interval preserving order adjoints

Positivity, vol. 29

Abstract

Abstract Riesz homomorphisms between vector lattices are characterized by interval preserving order adjoints. Buskes, van Rooij, and van Haandel generalized the notion of a Riesz homomorphism to linear maps between general ordered vector spaces. In this paper, we discuss how far the characterization between vector lattices extends to directed ordered vector spaces and pre-Riesz spaces.

Authors 4

1. Florian Boisen corresponding

   Technische Universität Dresden

   Affiliation as printed

   Fakultät Mathematik, Institut für Analysis, TU Dresden, Dresden, Germany

2. Anke Kalauch corresponding

   Technische Universität Dresden

   Affiliation as printed

   Fakultät Mathematik, Institut für Analysis, TU Dresden, Dresden, Germany

3. Janko Stennder corresponding

   Technische Universität Dresden

   Affiliation as printed

   Fakultät Mathematik, Institut für Analysis, TU Dresden, Dresden, Germany

4. Onno van Gaans corresponding Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University, Leiden, The Netherlands