A Monomial Basis for the Holomorphic Functions on $c_{0}$

TL;DR

This paper demonstrates that the spaces of holomorphic functions on c0, equipped with certain topologies, possess a monomial Schauder basis, advancing the understanding of their structural properties.

Contribution

It establishes the existence of a monomial Schauder basis for holomorphic function spaces on c0 under specific topologies, a novel structural result.

Findings

Spaces have a monomial Schauder basis

Applicable to $( au_{ ext{omega}})$ and $( au_{b})$ topologies

Enhances understanding of holomorphic function space structures

Abstract

We show that both $(\mathcal{H}(c_{0}),\tau_{\omega})$ and $(\mathcal{H}_{b}(c_{0}),\tau_{b})$ have a monomial Schauder basis.