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

 

$ C(K,\,E)$ contains a complemented copy of $ c\sb{0}$


Author: Pilar Cembranos
Journal: Proc. Amer. Math. Soc. 91 (1984), 556-558
MSC: Primary 46B25; Secondary 46E40
MathSciNet review: 746089
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Abstract: Let $ E$ be a Banach space and let $ K$ be a compact Hausdorff space. We denote by $ C(K,E)$ the Banach space of all $ E$-valued continuous functions defined on $ K$, endowed with the supremum norm. We prove in this paper that if $ K$ is infinite and $ E$ is infinite-dimensional, then $ C(K,E)$ contains a complemented subspace isomorphic to $ {c_0}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746089-2
PII: S 0002-9939(1984)0746089-2
Keywords: Complemented subspaces
Article copyright: © Copyright 1984 American Mathematical Society