@article {
author = {Moradi, S. and Honary, T. G. and Alimohammadi, D.},
title = {On the maximal ideal space of extended polynomial and rational uniform algebras},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {3},
number = {2},
pages = {1-12},
year = {2012},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {},
doi = {10.22075/ijnaa.2012.32},
abstract = {Let $K$ and $X$ be compact plane sets such that $K\subseteq X$. Let $P(K)$ be the uniform closure of polynomials on $K$. Let $R(K)$ be the closure of rational functions K with poles off $K$. Define $P(X,K)$ and $R(X,K)$ to be the uniform algebras of functions in $C(X)$ whose restriction to $K$ belongs to $P(K)$ and $R(K)$, respectively. Let $CZ(X,K)$ be the Banach algebra of functions $f$ in $C(X)$ such that $f|_K = 0$. In this paper, we show that every nonzero complex homomorphism' on $CZ(X,K)$ is an evaluation homomorphism $e_z$ for some $z$ in $X\setminus K$. By considering this fact, we characterize the maximal ideal space of the uniform algebra $P(X,K)$. Moreover, we show that the uniform algebra $R(X,K)$ is natural.},
keywords = {Maximal ideal space,uniform algebras,nonzero complex homomorphism},
url = {https://ijnaa.semnan.ac.ir/article_32.html},
eprint = {https://ijnaa.semnan.ac.ir/article_32_ded7ad00ddc06fb990aa09ff3ab151bd.pdf}
}