THE STABLE AND THE REAL RANK OF ${\mathcal Z}$-ABSORBING C*-ALGEBRAS
2004 ◽
Vol 15
(10)
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pp. 1065-1084
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Keyword(s):
Suppose that A is a C*-algebra for which [Formula: see text], where [Formula: see text] is the Jiang–Su algebra: a unital, simple, stably finite, separable, nuclear, infinite-dimensional C*-algebra with the same Elliott invariant as the complex numbers. We show that: (i) The Cuntz semigroup W(A) of equivalence classes of positive elements in matrix algebras over A is almost unperforated. (ii) If A is exact, then A is purely infinite if and only if A is traceless. (iii) If A is separable and nuclear, then [Formula: see text] if and only if A is traceless. (iv) If A is simple and unital, then the stable rank of A is one if and only if A is finite. We also characterize when A is of real rank zero.
1997 ◽
Vol 08
(03)
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pp. 383-405
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Keyword(s):
1996 ◽
Vol 39
(4)
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pp. 429-437
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2009 ◽
Vol 20
(10)
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pp. 1233-1261
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Keyword(s):
Keyword(s):
1992 ◽
Vol 03
(02)
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pp. 309-330
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Keyword(s):
2008 ◽
Vol 57
(7)
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pp. 3209-3240
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