Suppose that $A$ and $B$ are two linear operators on a separable, possibly infinite dimensional, Hilbert space $\mathcal{H}$. If both $A$ and $B$ are bounded, then one can use the triangle inequality to show that the commutator $AB-BA$ is also bounded. My question, then, is does there exist a Hilbert space $H$ and two operators $A, B \in \mathcal{B\mathcal{(H)}}$, with at least one of them unbounded, such that the commutator $AB-BA$ is bounded?
Note that if $A = \lambda B$ for some constant $\lambda$ then the answer is trivial.