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Consider a regular commutative, semisimple Banach algebra with a bounded approximate identity whose Gelfand transforms have compact support. A necessary and sufficient condition is given for a complex valued function defined on the maximal ideal space to determine a multiplier of the algebra. This theorem is similar to one proved by F. T. Birtel, but omits Birtel's assumption that the algebra be topologically embeddable in its second dual.

A necessary and sufficient condition that a function on the maximal ideal space of a Banach algebra be a multiplier