Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invertibility criterion in a C*-algebra acting on the Hardy space
  with applications to composition operators   In this paper we prove an invertibility criterion for certain operators which
is given as a linear algebraic combination of Toeplitz operators and Fourier
multipliers acting on the Hardy space of the unit disc. Very similar to the
case of Toeplitz operators we prove that such operators are invertible if and
only if they are Fredholm and their Fredholm index is zero. As an application
we prove that for "quasi-parabolic" composition operators the spectra and the
essential spectra are equal.

33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc