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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Multipliers for $ l\sb{1}$-algebras with approximate identities


Author: Charles D. Lahr
Journal: Proc. Amer. Math. Soc. 42 (1974), 501-506
MSC: Primary 43A10
DOI: https://doi.org/10.1090/S0002-9939-1974-0330922-6
MathSciNet review: 0330922
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Abstract: Let S be a commutative semigroup with multiplier semigroup $ \Omega (S)$. Assume that $ {l_1}(S)$ is semisimple and possesses a bounded approximate identity. If $ {l_1}{(S)^0}$ denotes the annihilator of $ {l_1}(S)$ in $ {l_1}(\Omega (S))$, then the multiplier algebra of $ {l_1}(S)$ is topologically isomorphic to $ {l_1}(\Omega (S))/{l_1}{(S)^0}$, and this quotient algebra of $ {l_1}(\Omega (S))$ is itself an $ {l_1}$-algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0330922-6
Keywords: Convolution measure algebra, $ {l_1}$-algebra, multiplier
Article copyright: © Copyright 1974 American Mathematical Society