RELATIVE K-THEORY FOR C∗-ALGEBRAS ∗-ALGEBRAS

Given C*-algebras A and B and a *-homomorphism phi : A -> B, we adopt the portrait of the relative K-theory K*(phi) due to Karoubi using Banach categories and Banach functors. We show that the elements of the relative groups may be represented in a simple form. We prove the existence of two six-term exact sequences, and we use these sequences to deduce the fact that the relative theory is isomorphic, in a natural way, to the K-theory of the mapping cone.