Illinois Journal of Mathematics

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

Jody Trout

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984842

Digital Object Identifier
doi:10.1215/ijm/1255984842

Mathematical Reviews number (MathSciNet)
MR1775323

Zentralblatt MATH identifier
0953.19002

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ijm/1255984842


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