Unbounded multipliers on commutative Banach algebras

In this paper the notion of an unbounded multiplier on a commutative Banach algebra is introduced. It is proven that, as in the case of bounded multipliers, unbounded multipliers also have Gelfand transforms. Some of the properties of these transforms are then developed. The final result of the paper is a new characterization of the bounded multipliers on A where A is a Banach algebra of the type described below. l Introduction * In general, by a multiplier on a commuta-tive Banach algebra A one means a bounded linear operator T: A-> A such that T(xy) = xT(y) for all x, y eA. There is an extensive literature on the subject. One can consult, for example, [2] and [3]. There does not seem to be, however, a systematic treatmen