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.
Moradi, S., Honary, T. G. & Alimohammadi, D. (2012). On the maximal ideal space of extended polynomial and rational uniform algebras. International Journal of Nonlinear Analysis and Applications, 3(2), 1–12. https://doi.org/10.22075/ijnaa.2012.32
MLA
Moradi, S., Honary, T. G., & Alimohammadi, D. "On the maximal ideal space of extended polynomial and rational uniform algebras", International Journal of Nonlinear Analysis and Applications, 3, 2, 2012, 1–12. doi: 10.22075/ijnaa.2012.32
HARVARD
Moradi, S., Honary, T. G., & Alimohammadi, D. (2012). 'On the maximal ideal space of extended polynomial and rational uniform algebras', International Journal of Nonlinear Analysis and Applications, 3(2), pp. 1–12. doi: 10.22075/ijnaa.2012.32
CHICAGO
Moradi, S., Honary, T. G. & Alimohammadi, D., "On the maximal ideal space of extended polynomial and rational uniform algebras." International Journal of Nonlinear Analysis and Applications, 3 2 (2012): 1–12, doi: 10.22075/ijnaa.2012.32
VANCOUVER
Moradi S., Honary T. G., Alimohammadi D. On the maximal ideal space of extended polynomial and rational uniform algebras. IJNAA. 2012;3(2):1–12. doi: 10.22075/ijnaa.2012.32
International Journal of Nonlinear Analysis and Applications