The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916059195375616 |
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| author | Boisen, Florian Kalauch, Anke Kuo, Wen-Chi Stennder, Janko Watson, Bruce A. |
| author_facet | Boisen, Florian Kalauch, Anke Kuo, Wen-Chi Stennder, Janko Watson, Bruce A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$ Boisen, Florian Kalauch, Anke Kuo, Wen-Chi Stennder, Janko Watson, Bruce A. Functional Analysis Probability 46A40, 46E40, 46G10, 47B60, 47B65 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. |
| title | The $T$-strong duals of $L^1(T)$ and $L^\infty(T)$ |
| topic | Functional Analysis Probability 46A40, 46E40, 46G10, 47B60, 47B65 |
| url | https://arxiv.org/abs/2605.29650 |