Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On universal spaces for the class of Banach spaces whose dual balls are
  uniform Eberlein compacts   For k being the first uncountable cardinal w_1 or k being the cardinality of
the continuum c, we prove that it is consistent that there is no Banach space
of density k in which it is possible to isomorphically embed every Banach space
of the same density which has a uniformly G\^ateaux differentiable renorming
or, equivalently, whose dual unit ball with the weak* topology is a subspace of
a Hilbert space (a uniform Eberlein compact space). This complements a
consequence of results of M. Bell and of M. Fabian, G. Godefroy, V. Zizler that
assuming the continuum hypothesis, there is a universal space for all Banach
spaces of density k=c=w_1 which have a uniformly G\^ateaux differentiable
renorming. Our result implies, in particular, that \beta N-N may not map
continuously onto a compact subset of a Hilbert space with the weak topology of
density k=w_1 or k=c and that a C(K) space for some uniform Eberlein compact
space K may not embed isomorphically into l_\infty/c_0.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess