Let A be a normed algebra
and B(A) the algebra of all bounded linear operators from A into itself,
with operator norm. An element T ∈ B(A) is called a multiplier of A if
(Tx)y = x(Ty) for all x,y ∈ A. The set of all multipliers of A is denoted by M(A). In
the present paper, it is first shown that M(A) is a maximal commutative
subalgebra of B(A) if and only if A is commutative. Next, M(A) in case A is an
H∗-algebra wi# l be represented as the algebra of all complexvalued functions
on certain discrete space. Finally, as an application of the representation
theorem of M(A), the set of all compact multipliers of compact H∗-algebras is
characterized.
