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

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 $(0,\infty )$.

17 pages. arXiv admin note: text overlap with arXiv:2104.13077