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

Harvard

Haagerup, U 2014, 'Quasitraces on exact C*-algebras are traces', Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, bind 36, nr. 2-3, s. 67-92.

APA

Haagerup, U. (2014). Quasitraces on exact C*-algebras are traces. Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, 36(2-3), 67-92.

Vancouver

Haagerup U. Quasitraces on exact C*-algebras are traces. Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science. 2014;36(2-3):67-92.

Author

Haagerup, Uffe. / Quasitraces on exact C*-algebras are traces. I: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science. 2014 ; Bind 36, Nr. 2-3. s. 67-92.

Bibtex

@article{2c88f87a6e3b47f3885ed1440a0e3966,
title = "Quasitraces on exact C*-algebras are traces",
abstract = "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 R{\o}rdam to prove that RR(A)=0  for every simple non-commutative torus of any dimension",
author = "Uffe Haagerup",
year = "2014",
language = "English",
volume = "36",
pages = "67--92",
journal = "Mathematical Reports of the Academy of Science",
issn = "0706-1994",
publisher = "Royal Society of Canada",
number = "2-3",

}

RIS

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