  We study the change of quantization for a class of global pseudodifferential
operators of infinite order in the setting of ultradifferentiable functions of
Beurling type. The composition of different quantizations as well as the
transpose of a quantization are also analysed, with applications to the Weyl
calculus. We also compare global $\omega$-hypoellipticity and global
$\omega$-regularity of these classes of pseudodifferential operators.
