Let A be a C*-algebra and A** its enveloping W'-algebra. Let LM(/4) be the left multipliers of A , RM(A) the right multipliers of A and QM(/1) the quasi-multipliers of A . A question was raised by Akemann and Pedersen [1] whether QM(A) = LM{A) + RM(A). McKennon [20] gave a nonseparable counterexample. L. Brown [6] shows the answer is negative for stable (separable) C*-algebras also. In this paper, we mainly consider cr-unitial C*-algebras. We give a criterion for QM(/1) = IM(A)+RM(A). In the

more »

... e that A is stable, we give a necessary and sufficient condition for QM(A) = LM(A) + RM(/4). We also give answers for other C*-algebras.