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March 25, 2015 By

Quasitraces are traces: A short proof of the finite-nuclear-dimension case

C. R. Math. Rep. Acad. Sci. Canada Vol. 33 (2) 2011, pp. 44–49

June 30, 2011

Nathanial P. Brown, Department of Mathematics, Penn State University, State College, PA 16802, USA; e-mail: nbrown@math.psu.edu

Wilhelm Winter, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK; e-mail: wilhelm.winter@nottingham.ac.uk

Abstract/Résumé:

Uffe Haagerup proved that quasitraces on unital exact \(C^*\)-algebras are traces. We give a short proof under the stronger hypothesis of locally finite nuclear dimension; our result generalizes to the case of lower semicontinuous extended quasitraces on nonunital \(C^*\)-algebras.

Uffe Haagerup a démontré qu’une quasi-trace sur une \(C^*\)-algèbre exacte à élément unité est une trace. Nous donnons une courte démonstration sous l’hypothèse plus forte de dimension nucléaire localement finie; ce résultat se généralise jusqu’au cas d’une quasi-trace étendue semicontinue inférieurement sur une \(C^*\)-algèbre sans élément unité.

Keywords:
AMS Subject Classification: General theory of $C^*$-algebras 46L05

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