Complementation in Spaces of Continuous Functions on Compact Lines

Details Complementation in Spaces of Continuous Functions on Compact Lines Complementation in Spaces of Continuous Functions on Compact Lines

2011-05-21

arxiv.org/abs/1105.4262v2

Mathematics

Functional Analysis

25 pages, One reference added

Scientific paper

10.1016/j.jmaa.2011.07.057

We characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator, together with estimates of the norm of such an operator. This result is used to the study of strengthenings of the separable complementation property in spaces of continuous functions on compact lines. These properties include in particular continuous separable complementation property and existence of a projectional skeleton.

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