𝐶(𝐾,𝐸) contains a complemented copy of 𝑐₀

Cembranos, Pilar

doi:10.1090/S0002-9939-1984-0746089-2

$C(K, E)$ contains a complemented copy of $c_{0}$
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by Pilar Cembranos

Proc. Amer. Math. Soc. 91 (1984), 556-558

DOI: https://doi.org/10.1090/S0002-9939-1984-0746089-2

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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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