Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: \ell ^1-spreading models in mixed Tsirelson space   Suppose that (F_n)_{n=1}^{\infty} is a sequence of regular families of finite
subsets of N and (\theta_n)_{n=1}^{\infty} is a nonincreasing null sequence in
(0,1). The mixed Tsirelson space T[(\theta_{n}, F_n)_{n=1}^{\infty}] is the
completion of $c_{00}$ with respect to the implicitly defined norm ||x|| =
max{||x||_{c_0}, sup_n sup \theta_n \sum_{i=1}^{j}||E_{i}x||}, where the last
supremum is taken over all finite subsets E_{1},...,E_{j} of N such that E_1 <
>... <E_j and {min E_1,...,min E_j} \in F_n. Necessary and sufficient
conditions are obtained for the existence of higher order \ell ^1-spreading
models in every subspace generated by a subsequence of the unit vector basis of
T[(\theta_{n}, F_n)_{n=1}^{\infty}.

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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin