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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: James A. Wood
Journal: Proc. Amer. Math. Soc. 66 (1977), 38-40
MSC: Primary 46J05
MathSciNet review: 0450979
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0450979-4
PII: S 0002-9939(1977)0450979-4
Article copyright: © Copyright 1977 American Mathematical Society