Isometric classification of the $L^{p}$-spaces of infinite dimensional Lebesgue measure
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915652416045056 |
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| author | Rodríguez-Vidanes, Daniel L. Sampedro, Juan Carlos |
| author_facet | Rodríguez-Vidanes, Daniel L. Sampedro, Juan Carlos |
| contents | We investigate the isometric structure of $L^{p}$-spaces for the infinite-dimensional Lebesgue measure $(\mathbb{R}^{\mathbb{N}},μ)$. Under the continuum hypothesis (CH) we prove $L^{p}(μ)\cong \ell^{p}(\mathfrak{c},L^{p}[0,1])$, where $\mathfrak{c}$ denotes the cardinality of the continuum, and without CH we obtain an isometric, complemented copy of $\ell^{p}(\mathfrak{c},L^{p}[0,1])$ inside $L^{p}(μ)$. In a general framework, we characterize precisely when $L^{p}(ν)\cong \ell^{p}(κ,L^{p}[0,1])$ and classify all such isometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isometric classification of the $L^{p}$-spaces of infinite dimensional Lebesgue measure Rodríguez-Vidanes, Daniel L. Sampedro, Juan Carlos Functional Analysis 46B04, 28C20, 46G12 We investigate the isometric structure of $L^{p}$-spaces for the infinite-dimensional Lebesgue measure $(\mathbb{R}^{\mathbb{N}},μ)$. Under the continuum hypothesis (CH) we prove $L^{p}(μ)\cong \ell^{p}(\mathfrak{c},L^{p}[0,1])$, where $\mathfrak{c}$ denotes the cardinality of the continuum, and without CH we obtain an isometric, complemented copy of $\ell^{p}(\mathfrak{c},L^{p}[0,1])$ inside $L^{p}(μ)$. In a general framework, we characterize precisely when $L^{p}(ν)\cong \ell^{p}(κ,L^{p}[0,1])$ and classify all such isometries. |
| title | Isometric classification of the $L^{p}$-spaces of infinite dimensional Lebesgue measure |
| topic | Functional Analysis 46B04, 28C20, 46G12 |
| url | https://arxiv.org/abs/2503.06217 |