A nonlinear representation of dual spaces and its applications

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 $$H' = H {\rm and} (L^{p})' = L^{q}$$. Our proofs extend to a family of Orlicz spaces, and yield as an unexpected byproduct a version of the Helly–Hahn–Banach theorem.