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.
Publié le : 2000-06-15
Classification:
19K35,
46L80,
47A60,
47B48,
58J22
@article{1255984842,
author = {Trout, Jody},
title = {On graded $K$-theory, elliptic operators and the functional calculus},
journal = {Illinois J. Math.},
volume = {44},
number = {4},
year = {2000},
pages = { 294-309},
language = {en},
url = {http://dml.mathdoc.fr/item/1255984842}
}
Trout, Jody. On graded $K$-theory, elliptic operators and the functional calculus. Illinois J. Math., Tome 44 (2000) no. 4, pp. 294-309. http://gdmltest.u-ga.fr/item/1255984842/