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C(K, E) Contains a Complemented Copy of c0

Pilar Cembranos
Proceedings of the American Mathematical Society
Vol. 91, No. 4 (Aug., 1984), pp. 556-558
DOI: 10.2307/2044800
Stable URL: http://www.jstor.org/stable/2044800
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
C(K, E) Contains a Complemented Copy of c0
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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 c0.

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