Article contents
A Classification of Tsirelson Type Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
We give a complete classification of mixed Tsirelson spaces $T\left[ ({{F}_{i,}}{{\theta }_{i}})_{i=1}^{r} \right]$ for finitely many pairs of given compact and hereditary families
${{F}_{i}}$ of finite sets of integers and
$0<{{\theta }_{i}}<1$ in terms of the Cantor–Bendixson indices of the families
${{F}_{i}}$, and
${{\theta }_{i}}(1\le i\le r)$. We prove that there are unique countable ordinal
$\alpha $ and
$0<\theta <1$ such that every block sequence of
$T\left[ ({{F}_{i,}}{{\theta }_{i}})_{i=1}^{r} \right]$ has a subsequence equivalent to a subsequence of the natural basis of the
$T({{S}_{{{\omega }^{\alpha }}}},\theta )$. Finally, we give a complete criterion of comparison in between two of these mixed Tsirelson spaces.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2008
References
- 5
- Cited by