Abstract
Let X be a compact first countable space. In this paper we show that the set of isometries of C ( X ) that are involutions is algebraically reflexive. As a consequence of a recent work of Botelho and Jamison this leads to the conclusion that the set of generalized bi-circular projections on C ( X ) is also algebraically reflexive. We also consider these questions for the space C ( X , E ) where E is a uniformly convex Banach space.
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