2001/10/14 by Lorenz Halbeısen, Lorenz Halbeisen, Edward Odell +2
Mathematics · #05D05 #05D10 #46B20 #46B35 #46B45 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:05D05 #msc:05D10 #msc:46B20 #msc:46B35 #msc:46B45
paper · pdf · doi:10.48550/arxiv.math/0110146
33 pages
arxiv created 2001/10/14 · openalex publication_date 2001/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A well known application of Ramsey's Theorem to Banach Space Theory is the notion of a spreading model (e'i) of a normalized basic sequence (xi) in a Banach space X. We show how to generalize the construction to define a new creature (ei), which we call an asymptotic model of X. Every spreading model of X is an asymptotic model of X and in most settings, such as if X is reflexive, every normalized block basis of an asymptotic model is itself an asymptotic model. We also show how to use the Hindman-Milliken Theorem--a strengthened form of Ramsey's Theorem--to generate asymptotic models with a stronger form of convergence.