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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The representation of norm-continuous multipliers on $ L\sp{\infty }$-spaces


Author: Gregory A. Hively
Journal: Trans. Amer. Math. Soc. 184 (1973), 343-353
MSC: Primary 43A22
MathSciNet review: 0346425
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Abstract: If G is a group and $ {\mathcal{L}^\infty }(G,\mathcal{S})$ is an appropriate space of bounded measurable functions on G, a representation is obtained for the algebra of norm-continuous multipliers on $ {\mathcal{L}^\infty }(G,\mathcal{S})$ as an algebra of bounded additive set functions on G. If G is a locally compact group, a representation of the norm-continuous multipliers on the quotient space $ {\mathcal{L}^\infty }(G)$ is obtained in terms of a quotient algebra of bounded additive set functions on G.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0346425-2
Keywords: Group, locally compact group, bounded measurable function, left translation, multiplier, bounded additive set function, lifting, isometric algebraic isomorphism, representation
Article copyright: © Copyright 1973 American Mathematical Society