A necessary and sufficient condition that a function on the maximal ideal space of a Banach algebra be a multiplier
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- by James A. Wood PDF
- Proc. Amer. Math. Soc. 66 (1977), 38-40 Request permission
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.References
- Richard Arens, Operations induced in function classes, Monatsh. Math. 55 (1951), 1–19. MR 44109, DOI 10.1007/BF01300644
- F. T. Birtel, On a commutative extension of a Banach algebra, Proc. Amer. Math. Soc. 13 (1962), 815–822. MR 176349, DOI 10.1090/S0002-9939-1962-0176349-3
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 38-40
- MSC: Primary 46J05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0450979-4
- MathSciNet review: 0450979