We use recent work on spectral synthesis in multiplier algebras to give an intrinsic characterization of the separable C*-algebras A for which Orc(M(A)) = 1, i.e., for which the relation of inseparability on the topological space of primitive ideals of the multiplier algebra M(A) is an equivalence relation. This characterization has applications to the calculation of norms of inner derivations and other elementary operators on A and M(A). For example, we give necessary and sufficient conditions on the ideal structure of a separable C*-algebra A for the norm of every inner derivation to be twice the distance of the implementing element to the centre of M(A).
Archbold, R. J., & Somerset, D. W. B. (2014). Separation properties in the primitive ideal space of a multiplier algebra. Israel Journal of Mathematics, 200(1), 389-418. https://doi.org/10.1007/s11856-014-0022-6