An operator algebraic proof of Agler's factorization theorem

TL;DR

This paper presents a concise operator algebraic proof of Agler's factorization theorem, utilizing an operator algebra factorization theorem and offering insights into polynomial cases.

Contribution

It introduces a new, direct proof of Agler's theorem based on operator algebra techniques, enhancing understanding of these factorizations.

Findings

Provides a shorter proof of Agler's theorem

Offers detailed analysis of polynomial factorizations

Enhances theoretical understanding of operator algebra factorizations

Abstract

We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional information about these factorizations in the case of polynomials.