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

DOI: 10.2140/pjm.1977.69.333

Abstract

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

Milestones

Received: 11 November 1971

Published: 1 April 1977