Hahn-Banach type theorems for locally convex cones

We prove Hahn-Banach type theorems for linear functionals with values in R boolean OR {+infinity} on ordered cones. Using the concept of locally convex cones, we provide a sandwich theorem involving sub- and superlinear functionals which are allowed to attain infinite values. It renders general versions of well-known extension and separation results. We describe the range of all linear functionals sandwiched between given sub- and superlinear functionals on an ordered cone. The results are of interest even in vector spaces, since we consider sublinear functionals that may attain the value +infinity.