The local multiplier algebra of a C\(^*\)-algebra. II
[Part I by the author in Q. J. Math., Oxford (2) 47, No. 185, 123-132 (1996; Zbl 0857.43004).] Let \(A\) be a separable \(C^*\)-algebra and let \(M_{\text{loc}}(A)\) be its local multiplier algebra. It is shown that every minimal closed prime ideal of \(M_{\text{loc}}(A)\) is primitive. If the primitive ideal space of \(A\) has a dense \(G_\delta\) consisting of closed points (in particular, \(\text{Prim}(A)\) is a \(T_1\) space) and \(A\) is unital, then \(M_{\text{loc}}(A)\) is its own multiplier algebra and has only inner derivations.
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