# Gleason parts for algebras of holomorphic functions on the ball of $\mathbf{c_0}$

## TL;DR

This paper investigates the structure of Gleason parts within the maximal ideal space of algebras of bounded holomorphic functions on the unit ball of c_0, revealing insights into their complex geometry.

## Contribution

It provides a detailed analysis of Gleason parts for algebras of holomorphic functions on the ball of c_0, extending understanding of their maximal ideal spaces.

## Key findings

- Characterization of Gleason parts for $\
- on the ball of c_0
- Identification of the structure of the maximal ideal space $\

## Abstract

For a complex Banach space $X$ with open unit ball $B_X,$ consider the Banach algebras $\mathcal H^\infty(B_X)$ of bounded scalar-valued holomorphic functions and the subalgebra $\mathcal A_u(B_X)$ of uniformly continuous functions on $B_X.$ Denoting either algebra by $\mathcal A,$ we study the Gleason parts of the set of scalar-valued homomorphisms $\mathcal M(\mathcal A)$ on $\mathcal A.$ Following remarks on the general situation, we focus on the case $X = c_0.$