Complementation in Spaces of Continuous Functions on Compact Lines

Abstract

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.

25 pages, One reference added

References in corpus (1)

• Banach spaces with projectional skeletons

Cited by in corpus (7)

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• Almost disjoint families of countable sets and separable complementation properties
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• On extensions of $c_0$-valued operators
• On the class of continuous images of non-commutative Valdivia compacta
• Extension property and complementation of isometric copies of continuous functions spaces
• On the $c_0$-extension property for compact lines