Linearly ordered compacta and Banach spaces with a projectional resolution of the identity

Abstract

We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a Valdivia compact and every separable subspace of $C(K)$ is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos.

13 pages

Cited by in corpus (6)

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• Complementation in Spaces of Continuous Functions on Compact Lines
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• Almost disjoint families of countable sets and separable complementation properties
• The structure of Valdivia compact lines
• Extension property and complementation of isometric copies of continuous functions spaces