Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Asymptotically Symmetric Banach Spaces   We define and study asymptotically symmetric Banach spaces (a.s.) and its
variations: weakly a.s. (w.a.s.) and weakly normalized a.s. (w.n.a.s.). If X is
a.s. then all spreading models of X are uniformly symmetric. We show that the
converse fails. We also show that w.a.s. and w.n.a.s. are not equivalent
properties and that Schlumprecht's space S fails to be w.n.a.s. We show that if
X is separable and has the property that every normalized weakly null sequence
in X has a subsequence equivalent to the unit vector basis of c_0 then X is
w.a.s.. We obtain an analogous result if c_0 is replaced by ell_1 and also show
it is false if c_0 is replaced by ell_p, 1 < p < infinity. We prove that if 1
less than or equal p < infinity and the norm of the sum of (x_i)_1^n is of the
order n^{1/p} for all (x_i)_1^n in the n^{th} asymptotic structure of $X$, then
X contains an asymptotic ell_p, hence w.a.s. subspace.

28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th