TY - JOUR
ID - 32
TI - On the maximal ideal space of extended polynomial and rational uniform algebras
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Moradi, S.
AU - Honary, T. G.
AU - Alimohammadi, D.
AD - Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-
8-8349, Iran.
AD - Faculty of Mathematical Sciences and Computer Engineering, Teacher Train-
ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran.
Y1 - 2012
PY - 2012
VL - 3
IS - 2
SP - 1
EP - 12
KW - Maximal ideal space
KW - uniform algebras
KW - nonzero complex homomorphism
DO - 10.22075/ijnaa.2012.32
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_32.html
L1 - https://ijnaa.semnan.ac.ir/article_32_ded7ad00ddc06fb990aa09ff3ab151bd.pdf
ER -