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Zbl 0604.46040
Cembranos, Pilar
C(K,E) contains a complemented copy of $c\sb 0$. (English)
[J] Proc. Am. Math. Soc. 91, 556-558 (1984). ISSN 0002-9939; ISSN 1088-6826/e

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, the C(K,E) contains a complemented subspace isomorphic to $c\sb 0$.

MSC 2000:: *46E40 Spaces of vector-valued functions
46E15 Banach spaces of functions defined by smoothness properties
46B25 Classical Banach spaces in the general theory of normed spaces

Keywords: space of vector valued continuous functions; complemented subspace isomorphic to $c\sb 0$

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