On Graded K-theory, Elliptic Operators and the Functional Calculus

Abstract

Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group ${\hat{K}}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded Hilbert modules. An application to the index theory of elliptic differential operators on smooth closed manifolds and asymptotic morphisms is discussed.

arXiv comment14 pages texed

Cited by in corpus (1)

• The Cayley transform in complex, real and graded $K$-theory