Abstract Köthe spaces. III

Abstract

In this paper I shall be considering the space of linear maps between two (perfect) Riesz spaces, and shall show how certain topological properties of these maps are related to the natural order structure of the space. The fundamental result is (e) of section 4, certain special cases of which have been treated in (4) and (5), using a less elliptic method of proof. Probably the most interesting new result in the present paper is section 10 in the special case of both L and M× being L1 spaces (so that |σ| (L, L×) and |σ| (M×, M) are the norm topologies ((2 b), section 7) and Λ(L; M×) is the space of norm-continuous linear maps).