Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the complete separation of asymptotic structures in Banach spaces   Let $(e_i)_i$ denote the unit vector basis of $\ell_p$, $1\leq p< \infty$, or
$c_0$. We construct a reflexive Banach space with an unconditional basis that
admits $(e_i)_i$ as a uniformly unique spreading model while it has no subspace
with a unique asymptotic model, and hence it has no asymptotic-$\ell_p$ or
$c_0$ subspace. This solves a problem of E. Odell. We also construct a space
with a unique $\ell_1$ spreading model and no subspace with a uniformly unique
$\ell_1$ spreading model. These results are achieved with the utilization of a
new version of the method of saturation under constraints that uses sequences
of functionals with increasing weights.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph