Abstract: We examine the hypercyclicity of generalised derivations $S \mapsto AS-SB$, for fixed bounded linear operators $A, B$, on spaces of operators. Hitherto the principal result in this setting has been the characterisation of the hypercyclicity of the left and right multiplication operators by Bonet, Martínez-Giménez and Peris (2004).
The main example I will show is the existence of non-trivial hypercyclic generalised derivations on separable ideals of operators. I will also outline the somewhat surprising result that scalar multiples of the backward shift operator $cB$ never induce hypercyclic commutator maps $S \mapsto c\left(BS-SB\right)$ on separable ideals of operators on $\ell^2$.