Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On asymptotic models in Banach spaces   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 (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.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs