## Linear Dynamics and Derivations

#### Clifford Gilmore (University of Helsinki)

The primary goal is to examine the hypercyclicity of generalised derivations $$S \mapsto AS-SB$$, for fixed operators $$A,B$$, on spaces of operators. Hitherto the principle result in this setting has been the characterisation of the hypercyclicity of the left and right multipliers.
The main example I will show is the existence of non-trivial hypercyclic generalised derivations on separable ideals of operators. I will also outline how scalar multiples of the backward shift operator $$\lambda B$$, which is hypercyclic on the sequence space $$\ell^2$$ when $$|\lambda| > 1$$, never induce hypercyclic commutator maps $$S \mapsto \lambda\left(BS-SB\right)$$ on separable ideals of operators on $$\ell^2$$.