Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979317944
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