On Graded K-theory, Elliptic Operators and the Functional Calculus
نویسندگان
چکیده
Let A be a graded C∗-algebra. We characterize Kasparov’s K-theory group K̂0(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.
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