$O_M(\mathbb{R}^n)$ as locally convex Orlicz space

TL;DR

This paper provides a more direct proof of Valdivia's theorem on the space $O_M( eal^n)$, simplifying previous methods that relied on complex results from metric linear spaces and topological tensor products.

Contribution

The paper introduces a simplified, more direct proof of Valdivia's theorem, avoiding the use of advanced results from metric linear spaces and tensor product theory.

Findings

Simplified proof of Valdivia's theorem on $O_M( eal^n)$

Representation of $O_M$ as a locally convex Orlicz space

Elimination of reliance on complex existing results

Abstract

The original M.Valdivia proof of his theorem on representation of the space $O_M$ uses results of S.Rolewicz concerning metric linear spaces and results of A.Grothendieck from his theory of topological tensor product. We present a more direct proof.