Moradi, S., Honary, T., 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. doi: 10.22075/ijnaa.2012.32

S. Moradi; T. G. Honary; D. Alimohammadi. "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

Moradi, S., Honary, T., 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

Moradi, S., Honary, T., Alimohammadi, D. On the maximal ideal space of extended polynomial and rational uniform algebras. International Journal of Nonlinear Analysis and Applications, 2012; 3(2): 1-12. doi: 10.22075/ijnaa.2012.32

On the maximal ideal space of extended polynomial and rational uniform algebras

^{1}Department of Mathematics, Faculty of Science, Arak University, Arak, 38156- 8-8349, Iran.

^{2}Faculty of Mathematical Sciences and Computer Engineering, Teacher Train- ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran.

Abstract

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 rational functions K with poles o K. Dene 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 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 algebra P(X;K). Moreover, we show that the uniform algebra R(X;K) is natural.