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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.17704 |
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| _version_ | 1866912846208565248 |
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| author | Ezumi, Kazuki Lin, Min-Ruei Miura, Takeshi |
| author_facet | Ezumi, Kazuki Lin, Min-Ruei Miura, Takeshi |
| contents | Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto $S(C_0(Y))^+$ is a composition operator induced by a homeomorphism between $X$ and $Y$ . As a consequence, such a map extends to a surjective reallinear isometry from $C_0(X)$ onto $C_0(Y)$. We also characterize surjective phase-isometries on the positive unit sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17704 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A variant of Tingley's problem for positive unit spheres of continuous functions that vanish at infinity Ezumi, Kazuki Lin, Min-Ruei Miura, Takeshi Functional Analysis Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto $S(C_0(Y))^+$ is a composition operator induced by a homeomorphism between $X$ and $Y$ . As a consequence, such a map extends to a surjective reallinear isometry from $C_0(X)$ onto $C_0(Y)$. We also characterize surjective phase-isometries on the positive unit sphere. |
| title | A variant of Tingley's problem for positive unit spheres of continuous functions that vanish at infinity |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.17704 |