The local multiplier algebra of a C*-algebra, II

Let A be a separable C*-algebra and let M-loc(A) be the local multiplier al gebra of A. It is shown that every minimal closed prime ideal of M-loc(A) i s primitive. If Prim(A) has a dense G(delta) consisting of closed points (f or instance, if Prim(A) is a T-1-space) and A is unital, then M-loc(A) is i ts own local multiplier algebra and has only inner derivations. The same is true for M-loc(M-loc(A)) if A is non-unitial. If A is postliminal then M-l oc(M-loc((A)) is the regular sigma-completion of A, which is an AW*-algebra . (C) 2000 Academic Press.