  Let $H$ be a selfadjoint operator and $A$ a closed operator on a Hilbert
space $\mathcal{H}$. If $A$ is $H$-(super)smooth in the sense of Kato-Yajima,
we prove that $AH^{-\frac14}$ is $\sqrt{H}$-(super)smooth. This allows to
include wave and Klein-Gordon equations in the abstract theory at the same
level of generality as Schr\"{o}dinger equations.
  We give a few applications and in particular, based on the resolvent
estimates of Erdogan, Goldberg and Schlag \cite{ErdoganGoldbergSchlag09-a}, we
prove Strichartz estimates for wave equations perturbed with large magnetic
potentials on $\mathbb{R}^{n}$, $n\ge3$.
