Subnormal operators with compact selfcommutator
If $S$ is a hyponormal operator, then Putnam's inequality gives an estimate on the norm of the self-commutator $[S^*,S]$, while the Berger-Shaw theorem gives (under appropriate cyclicity hypotheses) a corresponding estimate on the trace of $[S^*,S]$. Of course these results hold when $S$ is subnormal. In the subnormal setting, the author obtains useful estimates on the norm and essential norm of
