Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biorthogonal systems in Banach spaces   We give biorthogonal system characterizations of Banach spaces that fail the
Dunford-Pettis property, contain an isomorphic copy of $c_0$, or fail the
hereditary Dunford-Pettis property. We combine this with previous results to
show that each infinite dimensional Banach space has one of three types of
biorthogonal systems.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci