In the present investigation, we obtain some subordination and superordination results for the Hadamard product of certain normalized analytic functions in the open unit disk involving the linear operator introduced in [J. Dziok and R. K. Raina, Demonstratio Math., 37 (3) (2004), 533–542]. Several consequences of the results are presented. It is also pointed out that one of the main results (Theorem 2.8 below) provides a corrected form of the proof stated in two recent known results