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A stability property of a class of Banach spaces not containing a complemented copy of $ l\sb{1}$


Authors: Elias Saab and Paulette Saab
Journal: Proc. Amer. Math. Soc. 84 (1982), 44-46
MSC: Primary 46B20; Secondary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1982-0633274-1
MathSciNet review: 633274
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633274-1
Keywords: Complemented subspaces, vector measures
Article copyright: © Copyright 1982 American Mathematical Society