We examine the question of when the *-homomorphism λ : A * D B → Ã * D̃ B̃ of full amalgamated free product C*-algebras, arising from compatible inclusions of C*-algebras A ⊆ Ã, B ⊆ B̃ and D ⊆ D̃, is an embedding. Results giving sufficient conditions for λ to be injective, as well as classes of examples where λ fails to be injective, are obtained. As an application, we give necessary and sufficient conditions for the full amalgamated free product of finite-dimensional. C*-algebras to be residually finite dimensional.
ASJC Scopus subject areas
- Applied Mathematics