Homomorphisms from the Fredholm Semigroup to Abelian Semigroups

C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (1) 2012, pp. 1–8

March 30, 2012

George A. Elliott, Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4; e-mail: elliott@math.toronto.edu

Brian Skinner, Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA; e-mail: bskinner@caltech.edu

Abstract/Résumé:

It is shown that the universal enveloping abelian semigroup of the semigroup of Fredholm operators on an infinite-dimensional Hilbert space is the group of integers.

On démontre que l’index de Fredholm est le morphisme universel du semigroupe d’opérateurs de Fredholm sur un espace de Hilbert de dimension infinie dans un semigroupe abélien.

Keywords: Fredholm index, Fredholm operators, Fredholm semigroup relative to a stable C*-algebra, abelian semi-group, semigroup homomorphisms
AMS Subject Classification: General theory of $C^*$-algebras 46L05

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