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arXiv · 2605.29650

The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$

Florian Boisen·Anke Kalauch·Wen-Chi Kuo·Janko Stennder·Bruce A. Watson
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Abstract

For a conditional expectation operator $T$ on a Dedekind complete Riesz space, we give representations of the $T$-strong duals of $L^1(T)$ and $L^\infty(T)$. The representation for the $T$-strong dual of $L^1(T)$ follows from the known result for $L^2(T)$. To describe the $T$-strong dual of $L^\infty(T)$, we introduce charges on components of weak order units and develop a corresponding integration theory.

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Florian Boisen, Anke Kalauch, Wen-Chi Kuo, Janko Stennder, Bruce A. Watson. 2026-05-28. The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$. https://arxiv.org/abs/2605.29650

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