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Proceedings of the American Mathematical Society

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A property of the embedding of $ c\sb 0$ in $ l\sb \infty$


Author: A. K. Snyder
Journal: Proc. Amer. Math. Soc. 97 (1986), 59-60
MSC: Primary 46A45; Secondary 40D25, 40H05
DOI: https://doi.org/10.1090/S0002-9939-1986-0831387-6
MathSciNet review: 831387
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Abstract: This note proves that if $ X$ is an FK space containing $ \{ {\delta ^n}\} $ and if $ X + {c_0} = {l_\infty }$, then $ X = {l_\infty }$. The result is stronger than the fact that $ {c_0}$ is not complemented in $ {l_\infty }$, and shows that separability can be dropped in a similar theorem of Bennett and Kalton. The proof depends on Schur's theorem and the fact that $ {l_\infty }$ is a GB space to show that $ X$ must be barrelled in $ {l_\infty }$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831387-6
Keywords: FK space, uncomplemented
Article copyright: © Copyright 1986 American Mathematical Society