Isomorphic classification of projective tensor products of spaces of continuous functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913733807177728 |
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| author | Causey, R. M. Galego, E. Samuel, C. |
| author_facet | Causey, R. M. Galego, E. Samuel, C. |
| contents | We prove that for infinite, countable, compact, Hausdorff spaces $K,L$, $C(K)\widehat{\otimes}_πC(L)$ is isomorphic to exactly one of the spaces $C(ω^{ω^ξ})\widehat{\otimes}_πC(ω^{ω^ζ})$, $0\leqslant ζ\leqslant ξ<ω_1$. We also prove that $C(K)\widehat{\otimes}_πC(L)$ is not isomorphic to $C(M)$ for any compact, Hausdorff space $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08271 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Isomorphic classification of projective tensor products of spaces of continuous functions Causey, R. M. Galego, E. Samuel, C. Functional Analysis We prove that for infinite, countable, compact, Hausdorff spaces $K,L$, $C(K)\widehat{\otimes}_πC(L)$ is isomorphic to exactly one of the spaces $C(ω^{ω^ξ})\widehat{\otimes}_πC(ω^{ω^ζ})$, $0\leqslant ζ\leqslant ξ<ω_1$. We also prove that $C(K)\widehat{\otimes}_πC(L)$ is not isomorphic to $C(M)$ for any compact, Hausdorff space $M$. |
| title | Isomorphic classification of projective tensor products of spaces of continuous functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2201.08271 |