Real parts of uniform algebras on the circle

W. P. Novinger

Vol. 57 (1975), No. 1, 259–264

DOI: 10.2140/pjm.1975.57.259

Abstract

This paper is about uniform algebras on the unit circle Γ in the complex plane and specifically with the spaces of real parts of such algebras. The major portion of the paper is devoted to proving that if A is the disc algebra on Γ and B is any uniform algebra on Γ such that ReA ⊂ ReB, then either B = C(Γ) or else B = A ∘ Φ(= {f ∘ Φ : f ∈ A}) for some homeomorphism Φ. We also show that any homeomorphism Φ for which ReA ⊂ ReA ∘ Φ must be absolutely continuous.

Mathematical Subject Classification 2000

Primary: 46J10

Milestones

Received: 17 July 1974

Revised: 27 August 1974

Published: 1 March 1975