Embedding of lattice cones into vector lattices. (English. Russian original) Zbl 0781.46012
Sov. Math. 35, No. 4, 1-7 (1991); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 4(347), 3-9 (1991).
In this paper (necessary and) sufficient conditions are presented in order that the linear span of a lattice cone be a vector lattice in which the original cone is embedded as a sublattice. In this respect the paper is a continuation of the work of B. Fuchssteiner and W. Lusky [“Convex cones”, North-Holland Math Stud. 56 (1981; Zbl 0478.46002)] and the article ‘Embedding theorems for cones and applications to classes of convex sets occurring to interval mathematic’ [Lect. Notes Comput. Sci. 212, 159-173 (1986; Zbl 0596.65028)] by K.D. Schmidt. The author also constructs examples which show that the linear span is in general not a vector lattice (albeit that it has the Riesz interpolation property).
Reviewer: C.B.Huijsmans (Leiden)
MSC:
| 46A40 | Ordered topological linear spaces, vector lattices |
| 06F20 | Ordered abelian groups, Riesz groups, ordered linear spaces |
