Title: Extending Edgar's ordering to locally convex spaces
Abstract: By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E *, and its topological dual by E ′. It is convenient to think of the elements of E as being linear functionals on E ′, so that E can be identified with a subspace of E ′*. The adjoint of a continuous linear map T : E → F will be denoted by T ′: F ′→ E ′. If 〈 E, F 〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α( E, F ), β( E, F ) and μ( E, F ) respectively.