Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutators of automorphic composition operators with adjoints   In this paper, we investigate the compactness of the commutator
$[C_\psi^{\ast}, C_\varphi]$ on the Hardy space $H^2(B_N)$ or the weighted
Bergman space $A^2_s(B_N)$ ($s>-1$), when $\varphi$ and $\psi$ are
automorphisms of the unit ball $B_N$. We obtain that $[C_\psi^{\ast},
C_\varphi]$ is compact if and only if $\varphi$ and $\psi$ commute and they are
both unitary. This generalizes the corresponding result in one variable.
Moreover, our technique is different and simpler. In addition, we also discuss
the commutator $[C_\psi^{\ast}, C_\varphi]$ on the Dirichlet space
$\mathcal{D}(B_N)$, where $\varphi$ and $\psi$ are linear fractional self-maps
or both automorphisms of $B_N$.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ