Abstract: The problems of embedding normed cones into normed linear spaces and the problems of extending continuous linear functionals from normed cones to normed linear spaces are studied in this paper. In the first part, by geometric methods, the embedding theorems of normed cones into normed linear spaces are proved directly. In the second part, for a convex cone in a given normed linear space, via the SHARPNESS MODULUS of the convex cone, the equivalent relation of the extension norm derived from the conical norm with the original norm is studied. The Hahn-Banach positive extension theorems of continuous linear functionals from normed cones to normed linear spaces are obtained at last.

Key words: Normed cone, Sharpness modulus of convex cone, Normed linear space, Embedding theorem, Positive extension