 More generally, if "M" is any vector subspace of L("X"; "W") such that "C" ∩ "M" is a proper cone, the ordering defined by "C" ∩ "M" is called the canonical ordering of "M".A linear map "u" between two preordered vector spaces "X" and "Y" with respective positive cones "C" and "D" is called positive if "u"("C") ⊆ "D".If "X" and "Y" are vector lattices with "Y" order complete and if "H" is the set of all positive linear maps from "X" into "Y" then the subspace "M"