Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An example of an asymptotically Hilbertian space which fails the
  approximation property   Following Davie's example of a Banach space failing the approximation
property [D], we show how to construct a Banach space E which is asymptotically
Hilbertian and fails the approximation property. Moreover, the space E is shown
to be a subspace of a space with an unconditional basis which is ``almost'' a
weak Hilbert space and which can be written as the direct sum of two subspaces
all of whose subspaces have the approximation property.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th