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A Classification of Tsirelson Type Spaces |
Canad. J. Math. 60(2008), 1108-1148
Published:2008-10-01
Printed: Oct 2008
Printed: Oct 2008
- J. Lopez-Abad
- A. Manoussakis
Abstract
We give a complete classification of mixed Tsirelson spaces
$T[(\mathcal F_i,\theta_i)_{i=1}^{r}]$ for finitely many pairs of
given compact and hereditary families $\mathcal F_i$ of finite sets of
integers and $0<\theta_i<1$ in terms of the Cantor--Bendixson indices
of the families $\mathcal F_i$, 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
$T[(\mathcal F_i,\theta_i)_{i=1}^{r}]$ has a subsequence equivalent to a
subsequence of the natural basis of the
$T(\mathcal S_{\omega^\alpha},\theta)$. Finally, we give a complete criterion of
comparison in between two of these mixed Tsirelson spaces.
| MSC Classifications: |
46B20 - Geometry and structure of normed linear spaces 05D10 - Ramsey theory [See also 05C55] |