Vol. 80, No. 1, 1979

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Functions which operate on the real part of a uniform algebra

Stuart Jay Sidney

Vol. 80 (1979), No. 1, 265–272

Three theorems are proved to the effect that a nonaffine function h on an interval cannot operate by composition on the real part of a uniform algebra on X unless the algebra is C(X). The additional hypotheses necessary are, respectively, that h be continuously differentiable, that h be “highly” nonaffine in a suitable sense, and that h operate in a rather weakly bounded manner. These results contain and extend work of J. Wermer and of A. Bernard.

Mathematical Subject Classification 2000
Primary: 46J10
Received: 15 January 1978
Published: 1 January 1979
Stuart Jay Sidney