Higher order spreading models

Volume 221 / 2013

S. A. Argyros, V. Kanellopoulos, K. Tyros 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.

Authors

  • S. A. ArgyrosDepartment of Mathematics
    Faculty of Applied Sciences
    National Technical University of Athens
    Zografou Campus
    15780, Athens, Greece
    e-mail
  • V. KanellopoulosDepartment of Mathematics
    Faculty of Applied Sciences
    National Technical University of Athens
    Zografou Campus
    15780, Athens, Greece
    e-mail
  • K. TyrosDepartment of Mathematics
    University of Toronto
    Toronto, Canada, M5S 2E4
    e-mail

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