Abstract
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.
Citation
Jody Trout. "On graded $K$-theory, elliptic operators and the functional calculus." Illinois J. Math. 44 (2) 294 - 309, Summer 2000. https://doi.org/10.1215/ijm/1255984842
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