  Let $u$ be the solution to the following stochastic evolution equation (1)
du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking
values in an Hilbert space $\HH$, where $L$ is a $\RR$ valued L\'evy process,
$A:H\to H$ an infinitesimal generator of a strongly continuous semigroup,
$\sigma:H\to \RR$ bounded from below and Lipschitz continuous, and $B:\RR\to H$
a possible unbounded operator. A typical example of such an equation is a
stochastic Partial differential equation with boundary L\'evy noise. Let
$\CP=(\CP_t)_{t\ge 0}$ %{\CP_t:0\le t<\infty}$ the corresponding Markovian
semigroup.
  We show that, if the system (2) du(t) = A u(t)\: dt + B v(t),\quad t>0 u(0) =
x is approximate controllable in time $T>0$, then under some additional
conditions on $B$ and $A$, for any $x\in H$ the probability measure
$\CP_T^\star \delta_x$ is positive on open sets of $H$. Secondly, as an
application, we investigate under which condition on %$\HH$ and on the L\'evy
process $L$ and on the operator $A$ and $B$ the solution of Equation [1] is
asymptotically strong Feller, respective, has a unique invariant measure. We
apply these results to the damped wave equation driven by L\'evy boundary
noise.
