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The Maximal Ideal Space of Subalgebras of the Disk Algebra

Published online by Cambridge University Press:  20 November 2018

Bruce Lund
Bruce Lund*
Affiliation:
Mathematics Department, University of New Brunswick Fredericton, N.B., Canada
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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)}.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 1 , April 1975 , pp. 61 - 65
Copyright
Copyright © Canadian Mathematical Society 1975

References

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