# Representations of dual spaces

## TL;DR

This paper introduces a nonlinear approach to representing dual spaces of Banach spaces, providing simplified proofs of classical theorems and extending to Orlicz spaces, also deriving a version of the Helly-Hahn-Banach theorem.

## Contribution

It presents a new nonlinear representation method for duals of Banach spaces, simplifying proofs and extending to Orlicz spaces, with an additional result on the Helly-Hahn-Banach theorem.

## Key findings

- Simplified proofs of $H'=H$ and $(L^p)'=L^q$ theorems
- Extension of representation to Orlicz spaces
- Derivation of a version of the Helly-Hahn-Banach theorem

## 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 $H'=H$ 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.