Functions which operate on the real part of a uniform algebra
S. J. Sidney · Pacific Journal of Mathematics · 1979
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 differentiate, 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.