  The fermionic second quantization operator $d\Gamma(B)$ is shown to be
bounded by a power $N^{s/2}$ of the number operator $N$ given that the operator
$B$ belongs to the $r$-th von Neumann-Schatten class, $s=2(r-1)/r$. Conversely,
number operator estimates for $d\Gamma(B)$ imply von Neumann-Schatten
conditions on $B$. Quadratic creation and annihilation operators are treated as
well.
