Vol. 57, No. 1, 1975

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Real parts of uniform algebras on the circle

W. P. Novinger

Vol. 57 (1975), No. 1, 259–264

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
Received: 17 July 1974
Revised: 27 August 1974
Published: 1 March 1975
W. P. Novinger