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On the structure of the set of higher order spreading models

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Sarı B., Tyros K.

Studia Mathematica

2014

tom 223

nr 2

149-173

We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $SM_{ξ}^{w}(X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $SM_{ξ}^{w}(X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $SM_{ξ}^{w}(X)$ is uncountable, then it contains an antichain of size continuum.

Ograniczanie wyników

1 Studia Mathematica

1 Sarı B.

1 Tyros K.

1 2014

Wyniki wyszukiwania

On the structure of the set of higher order spreading models