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