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arXiv · 2204.13904

Symmetric finite representability of $\ell^p$-spaces in rearrangement invariant spaces on $[0,1]$

Sergey V. Astashkin·Guillermo P. Curbera
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Abstract

For a separable rearrangement invariant space $X$ on $[0,1]$ of fundamental type we identify the set of all $p\in [1,\infty]$ such that $\ell^p$ is finitely represented in $X$ in such a way that the unit basis vectors of $\ell^p$ ($c_0$ if $p=\infty$) correspond to pairwise disjoint and equimeasurable functions. This can be treated as a follow up of a paper by the first-named author related to separable rearrangement invariant spaces on $(0,\infty)$.

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Sergey V. Astashkin, Guillermo P. Curbera. 2022-04-29. Symmetric finite representability of $\ell^p$-spaces in rearrangement invariant spaces on $[0,1]$. https://arxiv.org/abs/2204.13904

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