Finite order spreading models

2011/05/13 by Spiros A. Argyros, Argyros, S. A., Vassilis Kanellopoulos +3 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1105.2732

openalex publication_date 2011/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Extending the classical notion of the spreading model, the k-spreading models of a Banach space are introduced, for every k∈ℕ. The definition, which is based on the k-sequences and plegma families, reveals a new class of spreading sequences associated to a Banach space. Most of the results of the classical theory are stated and proved in the higher order setting. Moreover, new phenomena like the universality of the class of the 2-spreading models of c₀ and the composition property are established. As consequence, a problem concerning the structure of the k-iterated spreading models is solved.

Citations

• On a Problem of Formal Logic

Cited by

• On spaces admitting no ℓ_p or c₀ spreading model

Related

• Spreading Models in Banach Space Theory
• Higher Order Spreading Models
• On the structure of the spreading models of a Banach space
• Lattice structures and spreading models
• On the structure of the set of higher order spreading models