Representations of dual spaces

Abstract

We give a nonlinear representation of the duals for a class of Banach spaces. This leads to classroom-friendly proofs of the classical representation theorems $H^{\prime }=H$ and $(L^p{)}^{\prime }=L^q$. Our proofs extend to a family of Orlicz spaces, and yield as an unexpected byproduct a version of the Helly-Hahn-Banach theorem.

8 pages