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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Projection constants for $ C(S)$ spaces with the separable projection property


Author: John Warren Baker
Journal: Proc. Amer. Math. Soc. 41 (1973), 201-204
MSC: Primary 46B05; Secondary 46E15
MathSciNet review: 0320707
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Abstract: It is shown that if $ n$ and $ k$ are positive integers and $ C({\omega ^n}k)$ is the Banach space of continuous functions on the compact set $ \Gamma ({\omega ^n}k) = \{ \alpha \vert\alpha $ is an ordinal, $ \alpha \leqq {\omega ^n}k\} $ then $ C({\omega ^n}k) \in P'$ if and only if $ \gamma \leqq 2n + 1$. This establishes the value of the projection constant for all $ C(S)$ spaces possessing the separable projection property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0320707-8
PII: S 0002-9939(1973)0320707-8
Keywords: Banach spaces, continuous function spaces, separable projection property
Article copyright: © Copyright 1973 American Mathematical Society