Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation by analytic operator functions. Factorizations and very
  badly approximable functions   This is a continuation of our earlier paper \cite{PT3}. We consider here
operator-valued functions (or infinite matrix functions) on the unit circle
$\T$ and study the problem of approximation by bounded analytic operator
functions. We discuss thematic and canonical factorizations of operator
functions and study badly approximable and very badly approximable operator
functions.
  We obtain algebraic and geometric characterizations of badly approximable and
very badly approximable operator functions. Note that there is an important
difference between the case of finite matrix functions and the case of operator
functions. Our criteria for a function to be very badly approximable in the
case of finite matrix functions also guarantee that the zero function is the
only superoptimal approximant. However in the case of operator functions this
is not true.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
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
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc