Analytic equivalence among simply connected domains in 𝐶(𝑋)

Warren, Hugh E.

doi:10.1090/S0002-9947-1974-0358349-6

Analytic equivalence among simply connected domains in $C(X)$
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Trans. Amer. Math. Soc. 196 (1974), 265-288 Request permission

Abstract:

This work considers analytic equivalence within the analytic function theory for commutative Banach algebras which was introduced by E. R. Lorch. Necessary conditions of a geometric nature are given for simply connected domains in $C(X)$. These show that there are a great many equivalence classes. In some important cases, as when one domain is the unit ball, the given conditions are also sufficient. The main technique is the association of a simply connected domain in $C(X)$ with a family of Riemann surfaces over the plane.

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