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Copies of $ l\sb \infty$ in $ L\sp p(\mu;X)$


Author: José Mendoza
Journal: Proc. Amer. Math. Soc. 109 (1990), 125-127
MSC: Primary 46E40; Secondary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1990-1012935-3
MathSciNet review: 1012935
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Abstract: Let $ X$ be a Banach space and let $ (\Omega ,\sum ,\mu )$ be a measure space. For $ 1 \leq p < + \infty $ we denote by $ {L^p}(\mu ;X)$ the Banach space of all $ X$-valued Bochner $ p$-integrable functions on $ \Omega $. In this note we show that $ {L^p}(\mu ;X)$ contains an isomorphic copy of $ {l_\infty }$ if and only if $ X$ does.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1012935-3
Article copyright: © Copyright 1990 American Mathematical Society

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