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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.11463 |
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| _version_ | 1866911380513226752 |
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| author | Cúth, Marek Havelka, Jonáš Rondoš, Jakub Sarı, Bünyamin |
| author_facet | Cúth, Marek Havelka, Jonáš Rondoš, Jakub Sarı, Bünyamin |
| contents | We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$ satisfying either $T\geq 0$ or $T^{-1}\geq 0$. We also prove that for any compact spaces $K$ and $L$, the existence of a positive embedding $T: C(K) \to C(L)$ implies that the Cantor-Bendixson height of $K$ does not exceed the height of $L$. Furthermore, we introduce a one-sided positive Banach-Mazur distance and obtain new estimates for both the classical and positive distances. Notably, we prove the exact formula $d_{BM}(C(ω^{ω^α}), C(ω^{ω^αn})) = n+\sqrt{(n-1)(n+3)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The classification of $C(K)$ spaces for countable compacta by positive isomorphisms Cúth, Marek Havelka, Jonáš Rondoš, Jakub Sarı, Bünyamin Functional Analysis We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$ satisfying either $T\geq 0$ or $T^{-1}\geq 0$. We also prove that for any compact spaces $K$ and $L$, the existence of a positive embedding $T: C(K) \to C(L)$ implies that the Cantor-Bendixson height of $K$ does not exceed the height of $L$. Furthermore, we introduce a one-sided positive Banach-Mazur distance and obtain new estimates for both the classical and positive distances. Notably, we prove the exact formula $d_{BM}(C(ω^{ω^α}), C(ω^{ω^αn})) = n+\sqrt{(n-1)(n+3)}$. |
| title | The classification of $C(K)$ spaces for countable compacta by positive isomorphisms |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.11463 |