Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68223220120601On the maximal ideal space of extended polynomial and rational uniform algebras1123210.22075/ijnaa.2012.32ENS.MoradiDepartment of Mathematics, Faculty of Science, Arak University, Arak, 38156-
8-8349, Iran.T. G.HonaryFaculty of Mathematical Sciences and Computer Engineering, Teacher Train-
ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran.D.AlimohammadiDepartment of Mathematics, Faculty of Science, Arak University, Arak, 38156-
8-8349, Iran.Journal Article20110629Let K and X be compact plane sets such that K X. Let P(K)<br />be the uniform closure of polynomials on K. Let R(K) be the closure of rational<br />functions K with poles o K. Dene P(X;K) and R(X;K) to be the uniform<br />algebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),<br />respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) such<br />that fjK = 0. In this paper, we show that every nonzero complex homomorphism<br />' on CZ(X;K) is an evaluation homomorphism ez for some z in XnK. By con-<br />sidering this fact, we characterize the maximal ideal space of the uniform algebra<br />P(X;K). Moreover, we show that the uniform algebra R(X;K) is natural.https://ijnaa.semnan.ac.ir/article_32_ded7ad00ddc06fb990aa09ff3ab151bd.pdf