Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality of metric entropy   For two convex bodies K and T in $R^n$, the covering number of K by T,
denoted N(K,T), is defined as the minimal number of translates of T needed to
cover K. Let us denote by $K^o$ the polar body of K and by D the euclidean unit
ball in $R^n$. We prove that the two functions of t, N(K, tD) and N(D, tK^o),
are equivalent in the appropriate sense, uniformly over symmetric convex bodies
K in $R^n$ and over positive integers n. In particular, this verifies the
duality conjecture for entropy numbers of linear operators, posed by Pietsch in
1972, in the central case when either the domain or the range of the operator
is a Hilbert space.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph