$Sz(\cdot)\leqslant \omega^\xi$ is rarely a three space property
Functional Analysis
2020-01-01 v1
Abstract
We prove that for any non-zero, countable ordinal which is not additively indecomposable, the property of having Szlenk index not exceeding is not a three space property. This complements a result of Brooker and Lancien, which states that if is additively indecomposable, then having Szlenk index not exceeding is a three space property.
Keywords
Cite
@article{arxiv.1912.13429,
title = {$Sz(\cdot)\leqslant \omega^\xi$ is rarely a three space property},
author = {R. M. Causey},
journal= {arXiv preprint arXiv:1912.13429},
year = {2020}
}