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

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

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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

Information

Published: Summer 2000
First available in Project Euclid: 19 October 2009

zbMATH: 0953.19002
MathSciNet: MR1775323
Digital Object Identifier: 10.1215/ijm/1255984842

Subjects:
Primary: 19K35
Secondary: 46L80 , 47A60 , 47B48 , 58J22

Rights: Copyright © 2000 University of Illinois at Urbana-Champaign

Vol.44 • No. 2 • Summer 2000
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