Higher order spreading models

• Autorzy: S. A. Argyros , V. Kanellopoulos , K. Tyros
• Języki publikacji: EN

Abstrakty

EN

We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_{s})_{s∈ℱ}$ with 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 $(𝒮ℳ_{ξ}(X))_{ξ<ω₁}$. Each $𝒮ℳ_{ξ}(X)$ contains all spreading models generated by ℱ-sequences $(x_{s})_{s∈ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

Kategorie tematyczne

• 05D10: Ramsey theory
• 46B45: Banach sequence spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B06: Asymptotic theory of Banach spaces
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 221
• Numer: 1
• Strony: 23-68

Daty

wydano

2013

Twórcy

autor

S. A. Argyros

• Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

autor

V. Kanellopoulos

• Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

autor

K. Tyros

• Department of Mathematics, University of Toronto, Toronto, Canada, M5S 2E4

Identyfikatory

DOI

10.4064/fm221-1-2