A necessary and sufficient condition that a function on the maximal ideal space of a Banach algebra be a multiplier
Abstract: 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.
-  Richard Arens, Operations induced in function classes, Monatsh. Math. 55 (1951), 1–19. MR 0044109, https://doi.org/10.1007/BF01300644
-  F. T. Birtel, On a commutative extension of a Banach algebra, Proc. Amer. Math. Soc. 13 (1962), 815–822. MR 0176349, https://doi.org/10.1090/S0002-9939-1962-0176349-3
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