Copies of $l_ \infty$ in $L^ p(\mu ;X)$
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- by José Mendoza PDF
- Proc. Amer. Math. Soc. 109 (1990), 125-127 Request permission
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
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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