\(G\)-injective envelope of separable \(G\)-\(C^\ast\)-algebras (Q6619549)

The paper is concerned with an extension of a result of \textit{M. Argerami} and \textit{D. R. Farenick} [``Injective envelopes of separable C*-algebras'', Preprint, \url{arXiv:math/0506309}] to the G-equivariant setting where G is a discrete group acting on a separable C*-algebra by automorphisms. \textit{M. Hamana} [Tôhoku Math. J. (2) 37, 463--487 (1985; Zbl 0585.46053)] has shown that any G-C*-algebra admits a G-injective envelope containing the local multiplier algebra as well as the regular monotone completion of A as G-invariant subalgebras. The main result states that if any of these algebras is a W*-algebra then each of these algebras coincides with the others and is a direct sum of type I factors.