%0 Journal Article
%T On the maximal ideal space of extended polynomial and rational uniform algebras
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Moradi, S.
%A Honary, T. G.
%A Alimohammadi, D.
%D 2012
%\ 06/01/2012
%V 3
%N 2
%P 1-12
%! On the maximal ideal space of extended polynomial and rational uniform algebras
%K Maximal ideal space
%K uniform algebras
%K nonzero complex homomorphism
%R 10.22075/ijnaa.2012.32
%X Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras 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) suchthat fjK = 0. In this paper, we show that every nonzero complex homomorphism' on CZ(X;K) is an evaluation homomorphism ez for some z in XnK. By con-sidering this fact, we characterize the maximal ideal space of the uniform algebraP(X;K). Moreover, we show that the uniform algebra R(X;K) is natural.
%U https://ijnaa.semnan.ac.ir/article_32_ded7ad00ddc06fb990aa09ff3ab151bd.pdf