Many problems in operator theory lead to the consideration ofoperator equa- tions, either directly or via some reformulation. More often than t, how- ever, the underlying space is too 'small' to contain solutions of these equa- tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition- ally is enlarged to its (universal) enveloping von Neumann algebra A . This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A is thing other than the second dual space of A. Among the numerous fruitful applications of this principle is the well-kwn Kadison-Sakai theorem ensuring that every derivation 8 on a C*-algebra A becomes inner in A , though 8 may t be inner in A. The transition from A to A however is t an algebraic one (and cant be since it is well kwn that the property of being a von Neumann algebra cant be described purely algebraically). Hence, ifthe C*-algebra A is small in an algebraic sense, say simple, it may be inappropriate to move on to A . In such a situation, A is typically enlarged by its multiplier algebra M(A).