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

Authors: Florian Boisen, Anke Kalauch, Wen-Chi Kuo, Janko Stennder, Bruce A. Watson

math.FAmath.PR2026-05v1license

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.

Cite

@article{arxiv.2605.29650,
  title  = {The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$},
  author = {Florian Boisen and Anke Kalauch and Wen-Chi Kuo and Janko Stennder and Bruce A. Watson},
  journal= {arXiv preprint arXiv:2605.29650},
  year   = {2026}
}

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