  In this paper, we characterize hypercyclic generalized bilateral weighted
shift operators on the standard Hilbert module over the C*-algebra of compact
operators on the separable Hilbert space. Moreover, we give necessary and
sufficient conditions for these operators to be chaotic and we provide concrete
examples. In addition, we characterize a class of hypercyclic operators on
non-unital C*-algebras and we provide concrete examples.
