Vol. 69, No. 2, 1977

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A note on Edelstein’s iterative test and spaces of continuous functions

Jack Douglas Bryant and Thomas Francis McCabe

Vol. 69 (1977), No. 2, 333–335

In this note a question posed by Nadler is answered. It is shown that if X is a compact Hausdorff space that contains a sequence of distinct points that converge then there exists a linear contractive selfmap f of C(X) such that, for some x, the sequence of iterates {fn(x)} does not converge. In particular, the iterative test is not conclusive for c.

Mathematical Subject Classification 2000
Primary: 54H25
Received: 11 November 1971
Published: 1 April 1977
Jack Douglas Bryant
Thomas Francis McCabe