Topological methods for C^∗-algebras. I. Spectral sequences

Claude Schochet

Vol. 96 (1981), No. 1, 193–211

DOI: 10.2140/pjm.1981.96.193

Abstract

Let A be a C^∗-algebra filtered by an increasing sequence of closed ideals {A_n} with ∪_nA_n = A. Then there is a spectral sequence which converges to K_∗(A) and has E_p,∗¹ = K_∗(A_p∕A_p−1). More generally, such spectral sequences obtain for the Brown-Douglas-Fillmore functors ℰxt_∗(A), the Pimsner-Popa-Voiculescu functors ℰxt_∗(Y ;A), the Kasparov functors ℰxt_∗(A,B), or indeed for any sequence of covariant or contravariant functors on C^∗-algebras which satisfies an exactness axiom.

Mathematical Subject Classification 2000

Primary: 46M20

Secondary: 46L05, 58G12

Milestones

Received: 23 May 1980

Published: 1 September 1981