Geodesic
The Maximal Ideal Space of Subalgebras of the Disk Algebra
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 61-65

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a compact Hausdorff space and C(X) the complexvalued continuous functions on X. We say A is a function algebra on X if A is a point separating, uniformly closed subalgebra of C(X) containing the constant functions. Equipped with the sup-norm ‖f‖ = sup{|f(x)|: x ∊ X} for f ∊ A, A is a Banach algebra. Let MA denote the maximal ideal space.Let D be the closed unit disk in C and let U be the open unit disk. We call A(D)={f ∊ C(D):f is analytic on U} the disk algebra. Let T be the unit circle and set C1(T) = {f ∊ C(T): f'(t) ∊ C(T)}. 
Lund, Bruce. The Maximal Ideal Space of Subalgebras of the Disk Algebra. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 61-65. doi: 10.4153/CMB-1975-012-x
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[1] 1. Bjork, J.-E., Analytic structures in the maximal ideal space of a uniform algebra, Ark. Mat. 8 (1970), 239-244. Google Scholar

[2] 2. Bjork, J.-E., Holomorphic convexity and analytic structures in Banach algebras, Ark. Mat. 9 (1971), 39-54. Google Scholar

[3] 3. Gamelin, T. W., Polynomial approximation on thin sets, Symposium on Several Complex Variables, Park City, Utah, 1970. Springer-Verlag, Heidelberg (1971), 50-78. Google Scholar

[4] 4. Glicksberg, I., A remark on analyticity of function algebras, Pacific J. Math. 13 (1963), 1181-1185. Google Scholar

[5] 5. Goluzin, G. M., Geometric Theory of Functions of a Complex Variable, 26, Translations of Mathematical Monographs. American Math Society, Providence, R.I., 1969. Google Scholar

[6] 6. Lund, B., Ideals and subalgebras of a function algebra, Canad. J. Math., 26, (1974), 405-411. Google Scholar

[7] 7. Newman, M. H. A., Topology of Plane Sets. Cambridge University Press, Cambridge, U.K., 1954. Google Scholar

[8] 8. Novinger, W. P., Holomorphic functions with infinitely dijferentiable boundary values, Ill. J. Math. 15 (1971), 80-90. Google Scholar

[9] 9. Stout, E., The Theory of Uniform Algebras. Bogden and Quigley, Tarry town-on-Hudson, 1971. Google Scholar

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