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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.09296 |
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| _version_ | 1866911807915950080 |
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| author | de Jeu, Marcel van der Walt, Jan Harm |
| author_facet | de Jeu, Marcel van der Walt, Jan Harm |
| contents | It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of $\mathrm C(X)$ for a realcompact space $X$, when supplied with the Arens product, is isomorphic as an $f$-algebra to $\mathrm C(\tilde X)$ for some realcompact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09296 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The order bidual of C(X) for a realcompact space de Jeu, Marcel van der Walt, Jan Harm Functional Analysis 46E05, 46A40, 46M40 It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$, supplied with the Arens product, is isometrically isomorphic as a Banach algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism. We establish a similar result for realcompact spaces: The order bidual of $\mathrm C(X)$ for a realcompact space $X$, when supplied with the Arens product, is isomorphic as an $f$-algebra to $\mathrm C(\tilde X)$ for some realcompact space $\tilde X$. The space $\tilde X$ is unique up to homeomorphism. |
| title | The order bidual of C(X) for a realcompact space |
| topic | Functional Analysis 46E05, 46A40, 46M40 |
| url | https://arxiv.org/abs/2212.09296 |