  We prove that for any two projection operators $f,g$ on Hilbert space, their
anticommutator norm is given by the formula \[\|fg + gf\| = \|fg\| +
\|fg\|^2.\] The result demonstrates an interesting contrast between the
commutator and anticommutator of two projection operators on Hilbert space.
Specifically, the norm of the anticommutator $\|fg + gf\|$ is a simple
quadratic function of the norm $\|fg\|$ while the commutator norm $\|fg - gf\|$
is not a function of $\|fg\|$. Nevertheless, the result gives the following
bounds that are functions of $\|fg\|$ on the commutator norm: $\|fg\| -
\|fg\|^2 \le \|fg - gf\| \le \|fg\|$.
