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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11148 |
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| _version_ | 1866910452724793344 |
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| author | Oikhberg, Timur Tursi, Mary Angelica |
| author_facet | Oikhberg, Timur Tursi, Mary Angelica |
| contents | Suppose $X$ is a locally compact Polish space, and $G$ is a group of lattice isometries of $C_0(X)$ which satisfies certain conditions. Then we can equip $C_0(X)$ with an equivalent lattice norm $| \! | \! | \cdot | \! | \! |$ so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$. As an application, we show that for any locally compact Polish group $G$ there exists a locally compact Polish space $X$, and an lattice norm $| \! | \! | \cdot | \! | \! |$ on $C_0(X)$, so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice renormings of $C_0(X)$ spaces Oikhberg, Timur Tursi, Mary Angelica Functional Analysis 46B03, 46B04, 46B42, 46E05 Suppose $X$ is a locally compact Polish space, and $G$ is a group of lattice isometries of $C_0(X)$ which satisfies certain conditions. Then we can equip $C_0(X)$ with an equivalent lattice norm $| \! | \! | \cdot | \! | \! |$ so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$. As an application, we show that for any locally compact Polish group $G$ there exists a locally compact Polish space $X$, and an lattice norm $| \! | \! | \cdot | \! | \! |$ on $C_0(X)$, so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$. |
| title | Lattice renormings of $C_0(X)$ spaces |
| topic | Functional Analysis 46B03, 46B04, 46B42, 46E05 |
| url | https://arxiv.org/abs/2405.11148 |