Rotation Algebras and the Exel Trace Formula
2015 ◽
Vol 67
(2)
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pp. 404-423
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Keyword(s):
AbstractWe show that ifuandvare any two unitaries in a unitalC*–algebra such that ∥uv−vu∥ < 2 anduvu*v* commutes withuandv, then theC*–subalgebraAu,vgenerated by u and v is isomorphic to a quotient of some rotation algebraAθ, provided thatAu;vhas a unique tracial state. We also show that the Exel trace formula holds in any unitalC*–algebra. Let θ ∊ (−1/2, 1/2) be a real number. For any ∊ > 0; we prove that there exists ζ > 0 satisfying the following: if u and v are two unitaries in any unital simpleC*–algebra A with tracial rank zero such thatfor all tracial states τof A; then there exists a pair of unitariesandin A such that
2009 ◽
Vol 20
(10)
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pp. 1233-1261
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Keyword(s):
2017 ◽
Vol 09
(01)
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pp. 67-125
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Keyword(s):
2011 ◽
Vol 32
(2)
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pp. 785-807
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1989 ◽
Vol 41
(1)
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pp. 106-122
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Keyword(s):