  We show that the spaces of $A$-$m$-subharmonic and $B$-$m$-subharmonic
functions differ in sufficently high dimensions. We also prove that the
Monge-Amp\`ere type operator $\mathcal M_m$ associated to the space of
$m$-plurisubharmonic functions does not allow an integral comparison principle
except in the classical cases $m=1$ and $m=n$. These answer in the negative two
problems posed by A. Sadullaev.
