A+ CATEGORY SCIENTIFIC UNIT

On the structure of the set of higher order spreading models

Volume 223 / 2014

Bünyamin Sarı, Konstantinos Tyros Studia Mathematica 223 (2014), 149-173 MSC: 46B06, 46B25, 46B45. DOI: 10.4064/sm223-2-3

Abstract

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.

Authors

  • Bünyamin SarıDepartment of Mathematics
    University of North Texas
    Denton, TX 76203–5017, U.S.A.
    e-mail
  • Konstantinos TyrosMathematics Institute
    University of Warwick
    Coventry, CV4 7AL, UK
    e-mail

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