abstract
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On asymptotic models in Banach spaces

Lorenz Halbeisen and Edward Odell

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A well known application of Ramsey's Theorem to Banach Space Theory
is the notion of a spreading model (*ê*_{i}) of a normalized
basic sequence (*x*_{i}) in a Banach space *X*. We show how to
generalize the construction to define a new creature (*e*_{i}), 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.