Multipliers for $l_{1}$-algebras with approximate identities
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- by Charles D. Lahr
- Proc. Amer. Math. Soc. 42 (1974), 501-506
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330922-6
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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.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- 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