A dual representation theorem on the conditional Orlicz space generated from a random normed module
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912174853586944 |
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| author | Zhang, Xia Qian, Ke Liu, Ming |
| author_facet | Zhang, Xia Qian, Ke Liu, Ming |
| contents | In this paper, we first introduce the notion of a random Orlicz function, and further present the conditional Orlicz space generated from a random normed module. Second, we prove the denseness of the Orlicz heart of a random normed module $E$ in $E$ with respect to the $(\varepsilon, λ)$-topology. Finally, based on the above work, we establish a dual representation theorem on the conditional Orlicz space generated from a random normed module, which extends and improves some known results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dual representation theorem on the conditional Orlicz space generated from a random normed module Zhang, Xia Qian, Ke Liu, Ming Functional Analysis 46H25, 46E30, 46B20 In this paper, we first introduce the notion of a random Orlicz function, and further present the conditional Orlicz space generated from a random normed module. Second, we prove the denseness of the Orlicz heart of a random normed module $E$ in $E$ with respect to the $(\varepsilon, λ)$-topology. Finally, based on the above work, we establish a dual representation theorem on the conditional Orlicz space generated from a random normed module, which extends and improves some known results. |
| title | A dual representation theorem on the conditional Orlicz space generated from a random normed module |
| topic | Functional Analysis 46H25, 46E30, 46B20 |
| url | https://arxiv.org/abs/2501.00853 |