Apostol Algebras and Decomposition in Douglas Algebras

摘要

Let A be a function algebra. That is, A is a uniformly closed subalgebra of the space of continuous functions on a compact Hausdorff space Ω that separates the points in Ω and contains constant functions. We denote by M(A) and partial deriv A the maximal ideal space and the Shilov boundary of A, respectively. We identify a function in A with its Gelfand transform on M(A).