Banach Algebras and Several Complex Variables pp 131-136 | Cite as

# Generators

Chapter

## Abstract

Let 𝔄 be a uniform algebra on a compact space
the smallest closed subalgebra of 𝔄 which contains the constants and
and

*X.*Fix*f*_{1,}...,*f*_{k}∈ 𝔄 and denote, as earlier, by$$\left[ {{f_{1,...}}{f_{k\backslash }}|X} \right]$$

*f*_{1},...,*f*_{k}. If [*f*_{1},...*, f*_{ k }*|X*] = 𝔄, we say the*f*_{j}are a*set of generators*for 𝔄. In earlier sections we obtained criteria for a set*f*_{1}, ...,*f*_{k}to be a set of generators for the algebra*C(X).*Here we shall study the case when 𝔄 =*A*(*D*) the disk algebra, and more generally the case 𝔄 =*A*(*B*) where*B*is the closed ball in C^{ n }$${\left| {{z_1}} \right|^2} + ... + {\left| {{z_n}} \right|^2} \le 1$$

*A*(*B*) consists of all functions continuous in*B*and analytic in*B̊*.## Keywords

Singular Point Closed Unit Ball Uniform Algebra Analytic Disk Maximal Ideal Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Springer Science+Business Media New York 1976