On the structure of the set of higher order spreading models

• Autorzy: Bünyamin Sarı , Konstantinos Tyros
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B45: Banach sequence spaces
• 46B06: Asymptotic theory of Banach spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 223
• Numer: 2
• Strony: 149-173

Daty

wydano

2014

Twórcy

autor

Bünyamin Sarı

• Department of Mathematics, University of North Texas, Denton, TX 76203-5017, U.S.A.

autor

Konstantinos Tyros

• Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

Identyfikatory

DOI

10.4064/sm223-2-3