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Proceedings of the American Mathematical Society

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Complemented copies of $ c\sb 0$ in $ L\sp \infty(\mu,E)$


Author: Santiago Díaz
Journal: Proc. Amer. Math. Soc. 120 (1994), 1167-1172
MSC: Primary 46E40; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1994-1189744-1
MathSciNet review: 1189744
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Abstract: Let $ E$ be a Banach space, and let $ (\Omega ,\Sigma ,\mu )$ be a measure space. We denote by $ {L^\infty }(\mu ,E)$ the Banach space of all $ E$-valued $ \mu $-measurable essentially bounded functions on $ \Omega $, two functions being identified if they differ only on a locally $ \mu $-null set. We prove that if $ {L^\infty }(\mu ,E)$ contains a complemented copy of $ {c_0}$, then $ E$ contains a copy of $ {c_0}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1189744-1
Keywords: Essentially bounded functions, complemented copies of $ {c_0}$
Article copyright: © Copyright 1994 American Mathematical Society