Vol. 95, No. 2, 1981

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K-theory for commutants in the Calkin algebra

William Lindall Paschke

Vol. 95 (1981), No. 2, 427–434

Let A be a separable unital C-algebra, and let Bc be the commutant in the Calkin algebra of the image B of A under a trivial extension. We show that K0(Bc) is isomorphic to the group of invertibles in (weak) Ext of A and that, in the presence of an appropriate homotopy invariance assumption, K1(Bc) 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
Received: 2 June 1980
Published: 1 August 1981
William Lindall Paschke