In mathematics, the Hahn–Banach Theorem is a central tool in functional analysis. It allows the extension of bounded linear functionals defined on a subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed vector space to make the study of the dual space "interesting"
I need a short and excellent proof for Hahn–Banach theorem. Anyone could help me ?
The Hahn-Banach Theorem surveyed, by Gerard Buskes, Rozprawy Matematyczne contains a lot of different proofs of Hahn-Banach theorem and much more.