𝐿¹ₓ is weakly compactly generated if 𝑋 is

Diestel, J.

doi:10.1090/S0002-9939-1975-0367651-X

$L^{1}_{x}$ is weakly compactly generated if $X$ is
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Proc. Amer. Math. Soc. 48 (1975), 508-510 Request permission

Abstract:

Though good criteria for weak compactness in the space of Bochner-integrable functions are not yet known, one can show that ${L_1}(\mu ;X)$ is a weakly compactly generated Banach space whenever $\mu$ is finite and $X$ is a weakly compactly generated Banach space. The proof depends upon a recent factorization scheme due to W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński.

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Weak convergence in certain special Banach spaces

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