Isometries of $p$-convexified combinatorial Banach spaces
Volume 275 / 2024
Studia Mathematica 275 (2024), 197-234
MSC: Primary 46B04; Secondary 46B45, 03E05
DOI: 10.4064/sm230620-14-12
Published online: 29 May 2024
Abstract
We show that if $1 \lt p\neq 2 \lt \infty $, then any isometry of the $p$-convexification of the combinatorial Banach space associated to a hereditary family of finite subsets of $\mathbb{N}$ containing the singletons is given by a signed permutation of the canonical basis. In the case of a generalized Schreier family, the result also holds for $p=2$, and every isometry is diagonal. These results are deduced from more general theorems concerning combinatorial-like Banach spaces.
