Topological methods for<i>C</i>^∗-algebras. I. Spectral sequences

Abstract

Let A be a C*-algebra filtered by an increasing sequence of closed ideals {A n } with U n A n =A. Then there is a spectral sequence which converges to K*{A) and has El^^K^AJAp-t). More generally, such spectral sequences obtain for the Brown-Douglas-Fillmore functors &xt*(A), the Pimsner-Popa-Voiculescu functors &xt*(Y; A), the Kasparov functors &xt*(A, B), or indeed for any sequence of covariant or contravariant functors on C*-algebras which satisfies an exactness axiom.