Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distances between Banach spaces   The main object of the paper is to study the distance between Banach spaces
introduced by Kadets. For Banach spaces $X$ and $Y$, the Kadets distance is
defined to be the infimum of the Hausdorff distance $d(B_X,B_Y)$ between the
respective closed unit balls over all isometric linear embeddings of $X$ and
$Y$ into a common Banach space $Z.$ This is compared with the Gromov-Hausdorff
distance which is defined to be the infimum of $d(B_X,B_Y)$ over all isometric
embeddings into a common metric space $Z$. We prove continuity type results for
the Kadets distance including a result that shows that this notion of distance
has applications to the theory of complex interpolation.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
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
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga