In this paper, we give a necessary and sufficient condition for thecomposition operator Cφ on the weighted sequence space ℓp(λ) to be bounded.We also characterize the range space of composition operator Cφ and thenestablish a necessary and sufficient condition for range space of Cφ to be closed.We also determine the necessary and sufficient conditions for surjectivity andalso for injectivity of composition operator Cφ. Further, we exhibit conditionsfor hypercyclicity and supercyclicity for composition operators.