Vol. 62, No. 2, 1976

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Uniform algebras spanned by Hartogs series

Theodore William Gamelin

Vol. 62 (1976), No. 2, 401–417

Let A be a uniform algebra on a compact space X, and let R be an upper semi-continuous function from X to [0,). Let

Y  = {(x,ζ) ∈ X × C; |ζ| ≦ R (x )},

and let B be the uniform algebra on Y generated by polynomials in ζ with coefficients in A. The maximal ideal space MB of B then has the form

MB = {(φ,ζ) ∈ MA × C : |ζ| ≦ R˜(φ)}

for some function R on MA. We will give several characterizations of R in terms of R. One description involves Hartogs functions, another involves Jensen measures. We will also treat the problem of characterizing the continuous functions on MB which lie in the algebra B.

Mathematical Subject Classification 2000
Primary: 46J10
Received: 21 May 1975
Published: 1 February 1976
Theodore William Gamelin