Weak compactness in 𝐿¹(𝜇,𝑋)

Díaz, Santiago

doi:10.1090/S0002-9939-96-03336-9

Weak compactness in $L^1(\mu ,X)$
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by Santiago Díaz

Proc. Amer. Math. Soc. 124 (1996), 2685-2693

DOI: https://doi.org/10.1090/S0002-9939-96-03336-9

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Abstract:

We characterize weak compactness and weak conditional compactness of subsets of $L^{1}(\mu ,X)$ in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.

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