THE STRUCTURE OF QUASI-MULTIPLIERS OF C*-ALGEBRAS
Let A be a C*-algebra, A** its enveloping w*-algebra. Let LM(A) = x (ELEM) A**, xa (ELEM) A, for all a (ELEM) A RM(A) = x (ELEM) A**, ax (ELEM) A, for all a (ELEM) A , QM(A) = x (ELEM) A**, a x b (ELEM) A, for all a,b (ELEM) A . A question was raised by Akemann and Pederson 1 whether QM(A) = LM(A) + RM(A). McKennon 23 gave a non-separable counterexample. L. Brown 6 shows the answer is negative fo stable C*-algebras also. In this theis, we mainly consider (sigma)-unital C*-algebras. We give a criterion for QM(A) = LM(A) + RM(A). In the case that A is stable, we give a necessary and sufficient condition for QM(A) = LM(A) + RM(A). We also give answers for other C*-algebras.
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