Quasitraces on exact C*-algebras are traces
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Quasitraces on exact C*-algebras are traces. / Haagerup, Uffe.
I: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, Bind 36, Nr. 2-3, 2014, s. 67-92.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Quasitraces on exact C*-algebras are traces
AU - Haagerup, Uffe
PY - 2014
Y1 - 2014
N2 - It is shown that all 2-quasitraces on a unital exact C ∗ -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗ -algebra has a tracial state, and (2) if an AW ∗ -factor of type II 1 is generated (as an AW ∗ -algebra) by an exact C ∗ -subalgebra, then it is a von Neumann II 1 -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0 for every simple non-commutative torus of any dimension
AB - It is shown that all 2-quasitraces on a unital exact C ∗ -algebra are traces. As consequences one gets: (1) Every stably finite exact unital C ∗ -algebra has a tracial state, and (2) if an AW ∗ -factor of type II 1 is generated (as an AW ∗ -algebra) by an exact C ∗ -subalgebra, then it is a von Neumann II 1 -factor. This is a partial solution to a well known problem of Kaplansky. The present result was used by Blackadar, Kumjian and Rørdam to prove that RR(A)=0 for every simple non-commutative torus of any dimension
M3 - Journal article
VL - 36
SP - 67
EP - 92
JO - Mathematical Reports of the Academy of Science
JF - Mathematical Reports of the Academy of Science
SN - 0706-1994
IS - 2-3
ER -
ID: 137628477