Complemented copies of 𝑐₀ in 𝐿^{∞}(𝜇,𝐸)

Díaz, Santiago

doi:10.1090/S0002-9939-1994-1189744-1

Complemented copies of $c_ 0$ in $L^ \infty (\mu ,E)$
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by Santiago Díaz

Proc. Amer. Math. Soc. 120 (1994), 1167-1172

DOI: https://doi.org/10.1090/S0002-9939-1994-1189744-1

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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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