THE OPERATOR<i>K</i>-FUNCTOR AND EXTENSIONS OF<i>C</i>*-ALGEBRAS

Abstract

In this paper a general operator K-functor is constructed, depending on a pair A, B of C*-algebras. Special cases of this functor are the ordinary cohomological K-functor K*(B) and the homological K-functor K*(A). The results (homotopy invariance, Bott periodicity, exact sequences, etc.) permit one to compute effectively in concrete examples. The main result, concerning extensions of C*-algebras, consists in a description of a "stable type" of extensions of the most general form: . It is shown that the sum of such an extension with a fixed decomposable extension of the form is uniquely determined by an element of the group .