Extension theorems with the range space not necessarily Dedekind complete

Abstract

We show that every positive linear operator from a majorizing subspace of a separable Fréchet lattice into a Hausdorff locally solid Riesz space with the Fatou property and the σ interpolation property can be extended. We shall also characterize the extreme points of the convex set of all positive linear extensions of a positive linear operator defined on a vector subspace when the range space is not assumed to be Dedekind complete.