Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic property of Schachermayer's space under renorming   A Banach space X with closed unit ball B is said to have property 2-beta,
repsectively 2-NUC if for every \ep > 0, there exists \delta > 0 such that for
every \ep-separated sequence (x_n) in the unit ball B, and every x in B, there
are distinct indices m and n such that ||x + x_m + x_n|| < 3(1 - \delta),
respectively, ||x_m + x_n|| < 2(1 - \delta). It is shown that a Banach space
constructed by Schachermayer has property 2-beta but cannot be renormed to have
property 2-NUC.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin