K-theory for commutants in the Calkin algebra

William Lindall Paschke

Vol. 95 (1981), No. 2, 427–434

DOI: 10.2140/pjm.1981.95.427

Abstract

Let A be a separable unital C^∗-algebra, and let B^c be the commutant in the Calkin algebra of the image B of A under a trivial extension. We show that K₀(B^c) is isomorphic to the group of invertibles in (weak) Ext of A and that, in the presence of an appropriate homotopy invariance assumption, K₁(B^c) is isomorphic to Ext of the reduced suspension of A. These facts lead to an alternative approach to the Pimsner-Voiculescu exact sequence for Ext of a crossed product.

Mathematical Subject Classification 2000

Primary: 46M20

Secondary: 46L05

Milestones

Received: 2 June 1980

Published: 1 August 1981