Fundamental approximate identities and quasi-multipliers of simple AF \(C^*\)-algebras
Let A be a \(C^*\)-algebra and \(A^{**}\) be its enveloping von Neumann algebra. An element \(x\in A^{**}\) is a multiplier of A if xa, ax\(\in A\) for all \(a\in A\), and x is a quasi-multiplier if axb\(\in A\) for all \(a,b\in A\). The author denoted the multipliers the left multipliers, the right multipliers and the quasi-multipliers by M(A), LM(A), RM(A) and QMA, respective. The question was raised by Akemann and Pedersen whether \(QM(A)=LM(A)+RM(A)\). L. G. Brown showed the relation between this problem and the problem of perturbations of \(C^*\)-algebras. This paper studies fundamental approximate identity as generation of stable \(C^*\)-algebras. Moreover the author answers the quasi multiplier question for separable simple AF \(C^*\)-algebras. He also finds applications to perturbation problems.
scientific article; zbMATH DE number 4111349
scientific article