Abstract: The author show that if A is a complex abelian Banach algebra with an identity,then the decomposability of T∈M(A),the set of all multipliers on A,implies that the corresponding multiplication operator T:M(A)→M(A) is decomposable;moreover,in the Hilbert algebras case the assumation that A is abelian and A has an identity can be released.Those results are partially answers to a question raised by K.B.Laursen and M.M.Neumann [5].

Key words:  , decomposable operators, Banach algebra, multipliers