1Department of Mathematics University of North Texas Denton, TX 76203–5017, U.S.A. 2Mathematics Institute University of Warwick Coventry, CV4 7AL, UK
Studia Mathematica, Tome 223 (2014) no. 2, pp. 149-173
We generalize some results concerning the classical notion of a spreading model to spreading models of order $\xi $. Among other results, we prove that the set $SM_\xi ^w(X)$ of $\xi $-order spreading models of a Banach space $X$ generated by subordinated weakly null $\mathcal {F}$-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $SM_\xi ^w(X)$ contains an increasing sequence of length $\omega $ then it contains an increasing sequence of length $\omega _1$. Finally, if $SM_\xi ^w(X)$ is uncountable, then it contains an antichain of size continuum.
Keywords:
generalize results concerning classical notion spreading model spreading models order among other results prove set order spreading models banach space generated subordinated weakly null mathcal sequences endowed pre partial order domination semilattice moreover contains increasing sequence length omega contains increasing sequence length omega finally uncountable contains antichain size continuum
Affiliations des auteurs :
Bünyamin Sarı
1
;
Konstantinos Tyros
2
1
Department of Mathematics University of North Texas Denton, TX 76203–5017, U.S.A.
2
Mathematics Institute University of Warwick Coventry, CV4 7AL, UK
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Bünyamin Sarı; Konstantinos Tyros. On the structure of the set
of higher order spreading models. Studia Mathematica, Tome 223 (2014) no. 2, pp. 149-173. doi: 10.4064/sm223-2-3
