Copies of l∞ in Lp(μ; X)

José Mendoza
Proceedings of the American Mathematical Society
Vol. 109, No. 1 (May, 1990), pp. 125-127
DOI: 10.2307/2048371
Stable URL: http://www.jstor.org/stable/2048371
Page Count: 3

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Let X be a Banach space and let (Ω, Σ, μ) be a measure space. For $1 \leq p < +\infty$ we denote by Lp(μ; X) the Banach space of all X-valued Bochner p-integrable functions on Ω. In this note we show that Lp(μ; X) contains an isomorphic copy of l∞ if and only if X does.