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On the maximal ideal space of extended polynomial and rational uniform algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 3، شماره 2، بهمن 2012، صفحه 1-12 اصل مقاله (364.26 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2012.32 | ||
| نویسندگان | ||
| S. Moradi* 1؛ T. G. Honary2؛ D. Alimohammadi1 | ||
| 1Department of Mathematics, Faculty of Science, Arak University, Arak, 38156- 8-8349, Iran. | ||
| 2Faculty of Mathematical Sciences and Computer Engineering, Teacher Train- ing University, 599 Taleghani Avenue, Tehran, 15618, I.R. Iran. | ||
| تاریخ دریافت: 23 خرداد 1390، تاریخ بازنگری: 13 خرداد 1391، تاریخ پذیرش: 26 خرداد 1391 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Maximal ideal space؛ uniform algebras؛ nonzero complex homomorphism | ||
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