A characterization of the Mackey topology 𝜏(𝐿^{∞},𝐿¹)

Nowak, Marian

doi:10.1090/S0002-9939-1990-0991705-6

A characterization of the Mackey topology $\tau (L^ \infty , L^ 1)$
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Proc. Amer. Math. Soc. 108 (1990), 683-689 Request permission

Abstract:

We give a description of the Mackey topology $\tau ({L^\infty },{L^1})$ for finite measures in terms of a family of norms defined by certain Young functions. As an application we obtain various topological characterizations of sequential convergence in $\tau ({L^\infty },{L^1})$. Moreover, we obtain a criterion for relative weak compactness in ${L^1}$ in terms of the integral functional defined by some Young function.

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