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C(K, E) Contains a Complemented Copy of c0
Proceedings of the American Mathematical Society
Vol. 91, No. 4 (Aug., 1984), pp. 556-558
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044800
Page Count: 3
You can always find the topics here!Topics: Banach space, Mathematical complements, Mathematical theorems, Hausdorff spaces, Mathematical sequences, Linear transformations, Series convergence, Projective geometry
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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.
Proceedings of the American Mathematical Society © 1984 American Mathematical Society