The Maximal Ideal Space of Subalgebras of the Disk Algebra

Abstract

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)}.