E-theory is a special case of KK-theory

Let A and B be $C^{\ast }$-algebras, A separable, and B $\sigma$-unital and stable. It is shown that there are natural isomorphisms $E(A,B)=KK(SA,Q(B))=[SA,Q(B)\otimes K]$, where $SA=C_0(0,1)\otimes A$, $[\cdot ,\cdot ]$ denotes the set of homotopy classes of -homomorphisms, $Q(B) = M(B)/B$isthegeneralizedCalkinalgebraandKdenotesthe$C^$-algebra of compact operators.