A stability property of a class of Banach spaces not containing a complemented copy of 𝑙₁

Saab, Elias; Saab, Paulette

doi:10.1090/S0002-9939-1982-0633274-1

A stability property of a class of Banach spaces not containing a complemented copy of $l_{1}$
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by Elias Saab and Paulette Saab

Proc. Amer. Math. Soc. 84 (1982), 44-46

DOI: https://doi.org/10.1090/S0002-9939-1982-0633274-1

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Abstract:

Let $E$ be a Banach space and $K$ be a compact Hausdorff space. The space $C(K,E)$ will stand for the Banach space of all continuous $E$-valued functions on $K$ equipped with the sup norm. It is shown that the space $E$ does not contain a complemented subspace isomorphic to ${l_1}$ if and only if $C(K,E)$ has the same property.

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Sur les espaces de Banach contenant

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