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Transactions of the American Mathematical Society

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The structure of quasimultipliers of $ C\sp *$-algebras


Author: Hua Xin Lin
Journal: Trans. Amer. Math. Soc. 315 (1989), 147-172
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9947-1989-0937248-3
MathSciNet review: 937248
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Abstract: Let $ A$ be a $ {C^\ast }$-algebra and $ {A^{\ast\ast}}$ its enveloping $ {W^\ast }$-algebra. Let $ {\text{LM}}(A)$ be the left multipliers of $ A$, $ {\text{RM}}(A)$ the right multipliers of $ A$ and $ {\text{QM}}(A)$ the quasi-multipliers of $ A$. A question was raised by Akemann and Pedersen [1] whether $ {\text{QM}}(A) = {\text{LM}}(A) + {\text{RM}}(A)$. McKennon [20] gave a nonseparable counterexample. L. Brown [6] shows the answer is negative for stable (separable) $ {C^\ast }$-algebras also.

In this paper, we mainly consider $ \sigma $-unitial $ {C^\ast }$-algebras. We give a criterion for $ {\text{QM}}(A) = {\text{LM}}(A) + {\text{RM}}(A)$. In the case that $ A$ is stable, we give a necessary and sufficient condition for $ {\text{QM}}(A) = {\text{LM}}(A) + {\text{RM}}(A)$. We also give answers for other $ {C^\ast }$-algebras.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0937248-3
Article copyright: © Copyright 1989 American Mathematical Society

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