Higher order spreading models
Volume 221 / 2013
Fundamenta Mathematicae 221 (2013), 23-68
MSC: Primary 46B03, 46B06, 46B25, 46B45; Secondary 05D10.
DOI: 10.4064/fm221-1-2
Abstract
We introduce higher order spreading models associated to a Banach space $X$. Their definition is based on $\mathcal {F}$-sequences $(x_s)_{s\in \mathcal {F}}$ with $\mathcal {F}$ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space $X$ form an increasing transfinite hierarchy $(\mathcal {SM}_\xi (X))_{\xi <\omega _1}$. Each $\mathcal {SM}_\xi (X)$ contains all spreading models generated by $\mathcal {F}$-sequences $(x_s)_{s\in \mathcal {F}}$ with order of $\mathcal {F}$ equal to $\xi $. We also study the fundamental properties of this hierarchy.
