Spectral invariance, K-theory isomorphism and an application to the differential structure of C^*-algebras

Abstract

The notion of spectral invariance of a locally convex *-algebra is defined by constructing the enveloping C^*-algebra and is characterized. It is shown that the spectral invariance induces §{\rm K}§-theory isomorphism at a general level. As an application, the differential structure of C^*-algebras is studied.