C. R. Math. Rep. Acad. Sci. Canada Vol. 29 (2) 2007, pp. 48–51
June 30, 2007
George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4; e-mail: elliott@math.toronto.edu
Abstract/Résumé:
It is shown that for countably generated Hilbert C\(^*\)-modules over a C\(^*\)-algebra of stable rank one (i.e., a C\(^*\)-algebra in which the invertible elements are dense) the relation of compact inclusion up to isomorphism is cancellative, in a certain weak but natural sense. This generalizes the well-known fact that cancellation is valid in the abelian semigroup of isomorphism classes of finitely generated projective modules over such a C\(^*\)-algebra.
Il est démontré que la relation d’inclusion compacte entre modules de Hilbert dénombrablement engendrés sur une C\(^*\)-algèbre de rang stable égal à un est cancellative, dans un sens faible mais naturel. Ceci généralise un résultat bien connu pour le cas des modules projectifs finiment engendrés.
AMS Subject Classification: General theory of $C^*$-algebras 46L05
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