Illinois Journal of Mathematics

On graded $K$-theory, elliptic operators and the functional calculus

Jody Trout

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Let $A$ be a graded $C^{\ast}$-algebra. We characterize Kasparov's $K$-theory group $\hat{K}_{0}(A)$ in terms of graded $\ast$-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.

Article information

Illinois J. Math., Volume 44, Issue 2 (2000), 294-309.

First available in Project Euclid: 19 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 19K35: Kasparov theory ($KK$-theory) [See also 58J22]
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 47A60: Functional calculus 47B48: Operators on Banach algebras 58J22: Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]


Trout, Jody. On graded $K$-theory, elliptic operators and the functional calculus. Illinois J. Math. 44 (2000), no. 2, 294--309. doi:10.1215/ijm/1255984842.

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