On the Proof of the Analytic Form of the Hahn Banach Theorem in Real Linear Spaces

Abstract

Let X be a real linear space and M be a proper subspace of X. Let p : X ! < be a sublinear functional on X and f : M ! < be a linear functional on M satisfying f(x) p(x) for all x 2 M. We observe that the proof of the well-de nedness of the upper bound functionals for chains in the set of linear functionals extending f, appears not to be plausible in many expositions. We put this aright.