Vol. 46, No. 1, 1973

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Real parts of uniform algebras

John M.F. O’Connell

Vol. 46 (1973), No. 1, 235–247
Abstract

This paper is concerned with identifying those uniform algebras B on Γ = {z : |z| = 1} for which ReB—the space of real parts of the functions in B—equals ReA, where A denotes the disk algebra. It is shown that for any such algebra, there is an absolutely continuous homeomorphism Φ of Γ onto Γ so that B = A(Φ) = {f(Φ) : f A}. A partial converse to this theorem also holds: If Φ is a homeomorphism of Γ onto itself which is of class C2 with nowhere vanishing derivative, then ReA(Φ) = ReA.

Mathematical Subject Classification 2000
Primary: 46J10
Milestones
Received: 23 July 1971
Published: 1 May 1973
Authors
John M.F. O’Connell