On Subalgebras of the Car-Algebra

Every nuclear unital separable C*-algebra A is unitally and completely isometrically ismorphic to the range of a unital completely positive projection on the CAR-algbra B = M2 ⊗ M2 ⊗ ···. Let C be a nuclearly imbeddable separable unital C*-algebra in the sense of Voiculescu [VO13]. Then there exists a C*-subalgebra E of the CAR-algebra B such that C is isomorphic to a quotient C*-algebra of E. We include one of the possible proofs that exact C*-algebras are nuclearly imbeddable. Proofs of G-covariant analogs are outlined for compact G. Some related results are obtained on non-selfadjoint operator algebras. The unital separable nuclear C*-algebras not of type I are mutually cb-isomorphic and have cb-distance ≤ 256. Separable Lindenstrauss spaces are isometric to quotients of the CAR-algebra by a sum of closed left and a closed right ideal.