An Analogue of the Hahn-Banach Theorem for Functionals on Abstract Convex Cones - Stonyakin, Fedor Sergeevich (Eurasian Mathematical Journal, 2016)
We prove an analogue of the Hahn-Banach theorem on the extension of a linear functional with a convex estimate for each abstract convex cone with the cancellation law. Also we consider the special class of the so-called strict convex normed cones (SCNC). For such structures we obtain an appropriate analogue of the Hahn-Banach separation theorem. On the base of this result we prove that each (SCNC) is sublinearly, injectively and isometrically embedded in some Banach space.