On a conjecture by Ghahramani-Lau and related problems concerning topological centres

Furthermore, the same condition used above implies that every linear left A**-module homomorphism on A* is automatically bounded and w*-continuous. We finally show that our criterion also yields a partial answer to a question raised by Lau-Ülger (Trans. Amer. Math. Soc. 348 (3) (1996) 1191) on the topological centre of the algebra (A*⊙A)*, for A having a right approximate identity bounded by 1.