The cluster value problem in spaces of continuous functions

TL;DR

This paper investigates the cluster value problem in Banach algebras of holomorphic functions on the unit ball of complex Banach spaces, focusing on spaces where X equals C(K).

Contribution

It provides new insights into the cluster value problem specifically for spaces of the form C(K), advancing understanding in this area.

Findings

Results established for the cluster value problem in C(K) spaces.

Extended the theoretical framework for holomorphic functions on Banach spaces.

Identified conditions under which the cluster value problem holds in these spaces.

Abstract

We study the cluster value problem for certain Banach algebras of holomorphic functions defined on the unit ball of a complex Banach space X. The main results are for spaces of the form X = C(K).