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Proceedings of the American Mathematical Society

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A characterization of the Mackey topology $ \tau(L\sp \infty, L\sp 1)$


Author: Marian Nowak
Journal: Proc. Amer. Math. Soc. 108 (1990), 683-689
MSC: Primary 46E30; Secondary 46A20
DOI: https://doi.org/10.1090/S0002-9939-1990-0991705-6
MathSciNet review: 991705
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-0991705-6
Keywords: Mackey topology $ \tau ({L^\infty },{L^1})$, Orlicz spaces, mixed topologies, locally solid Riesz spaces
Article copyright: © Copyright 1990 American Mathematical Society