Common extensions for linear operators
The main meaning of the common extension for two linear operators is the following: given two vector subspaces G₁ and G₂ in a vector space (respectively an ordered vector space) E, a Dedekind complete ordered vector space F and two (positive) linear operators T₁: G₁ → F, T₂: G₂ → F, when does a (positive) linear common extension L of T₁, T₂ exist? First, L will be defined on span(G₁ ∪ G₂). In other results, formulated in the line of the Hahn-Banach extension theorem, the common...