E-theory is a special case of KK-theory

الأصل · EN

Let A and B be C*-algebras, A separable, and B σ-unital and stable. It is shown that there are natural isomorphisms E(A,B)=KK(SA,Q(B))=[SA,Q(B)⊗ K], where SA=C₀(0,1)⊗ A, [·,·] denotes the set of homotopy classes of *-homomorphisms, Q(B) = M(B)/B is the generalized Calkin algebra and K denotes the C*-algebra of compact operators.