Geodesic
Higher order spreading models
S. A. Argyros 1   ; V. Kanellopoulos 1   ; K. Tyros 2
1 Department of Mathematics Faculty of Applied Sciences National Technical University of Athens Zografou Campus 15780, Athens, Greece
2 Department of Mathematics University of Toronto Toronto, Canada, M5S 2E4
Fundamenta Mathematicae, Tome 221 (2013) no. 1, pp. 23-68 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm221-1-2
Keywords: introduce higher order spreading models associated banach space nbsp their definition based mathcal sequences mathcal mathcal regular thin family plegma families higher order spreading models banach space form increasing transfinite hierarchy mathcal omega each mathcal contains spreading models generated mathcal sequences mathcal order mathcal equal study fundamental properties hierarchy

S. A. Argyros  1   ; V. Kanellopoulos  1   ; K. Tyros  2

1 Department of Mathematics Faculty of Applied Sciences National Technical University of Athens Zografou Campus 15780, Athens, Greece
2 Department of Mathematics University of Toronto Toronto, Canada, M5S 2E4 
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S. A. Argyros; V. Kanellopoulos; K. Tyros. Higher order spreading models. Fundamenta Mathematicae, Tome 221 (2013) no. 1, pp. 23-68. doi: 10.4064/fm221-1-2

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