C*-Algebras 2000
DOI: 10.1007/978-3-642-57288-3_5
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Random Matrices and Non-Exact C*-Algebras

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Cited by 38 publications
(78 citation statements)
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“…We use QT 2 (A) to denote the set of 2-quasitraces on A; see Section 5.2. By a famous result of Haagerup, [Haa14], every 2-quasitrace on a unital, exact C * -algebra is a trace. We let Lsc(QT 2 (A)) denote the set of lower-semicontinuous linear functions from the cone QT 2 (A) to [0, ∞].…”
Section: Almost Unperforated and Almost Divisible Cu-semigroupsmentioning
confidence: 99%
“…We use QT 2 (A) to denote the set of 2-quasitraces on A; see Section 5.2. By a famous result of Haagerup, [Haa14], every 2-quasitrace on a unital, exact C * -algebra is a trace. We let Lsc(QT 2 (A)) denote the set of lower-semicontinuous linear functions from the cone QT 2 (A) to [0, ∞].…”
Section: Almost Unperforated and Almost Divisible Cu-semigroupsmentioning
confidence: 99%
“…A very direct argument is indicated in Remark 4.5 below, but we prefer to base the proof on [9] in the style of [29] in order to make clear that it remains valid with matrix coefficients. By [29, (1.1)] applied twice (for k = 1) (see also Remark 1.5 in [29]) one finds for any even integer p…”
Section: Appendixmentioning
confidence: 99%
“…Since C * r (F n ) has a unique tracial state, it follows from Corollary 6.6 of [32] that C * r (F n ) ⊗ B has stable rank one. Moreover, C * r (F n ) ⊗ B is exact, so every quasitrace is a trace ( [11]), whence Theorem 7.2 of [33] implies that C * r (F n ) ⊗ B has real rank zero and Theorem 5.2(b) of [33] implies that the order on projections over C * r (F n ) ⊗ B is determined by traces. (In fact, K 0 (C * r (F n ) ⊗ B) is Z 1 2 with its usual order.)…”
Section: Examplesmentioning
confidence: 99%