  We define a family of star products and involutions associated with
$\kappa$-Minkowski space. Applying corresponding quantization maps we show that
these star products restricted to a certain space of Schwartz functions have
isomorphic Banach algebra completions. For two particular star products it is
demonstrated that they can be extended to a class of polynomially bounded
smooth functions allowing a realization of the full Hopf algebra structure on
$\kappa$-Minkowski space. Furthermore, we give an explicit realization of the
action of the $\kappa$-Poincar\'e algebra as an involutive Hopf algebra on this
representation of $\kappa$-Minkowski space and initiate a study of its
properties.
