A monomial basis for the holomorphic functions on 𝑐₀

Abstract

For over thirty years it has been known that the monomials form a basis for the n n -homogeneous polynomials on certain infinite dimensional Banach spaces. Recently, Defant and Kalton have shown that these are never unconditional. In this article we show that the monomials form a basis for both the holomorphic functions and the holomorphic functions of bounded type on c 0 c_{0} , both with their natural topologies.