# Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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## The structure of quasimultipliers of $C^ *$-algebrasHTML articles powered by AMS MathViewer

by Hua Xin Lin
Trans. Amer. Math. Soc. 315 (1989), 147-172 Request permission

## 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  whether ${\text {QM}}(A) = {\text {LM}}(A) + {\text {RM}}(A)$. McKennon  gave a nonseparable counterexample. L. Brown  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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