Dynamics of unbounded linear operators

We apply the well-known and also the newly introduced notions from bounded linear dynamics to unbounded linear operators. We present a hypermixing criterion similar to that given for bounded linear operators and then we show that the derivative operator in $H^2$, the Laplacian operator in $L^2(\mathrm{\Omega })$, and all unbounded weighted translations in $L_p(0,\mathrm{\infty })$ and $C_0[0,\mathrm{\infty })$ are hypermixing.