THE STABLE AND THE REAL RANK OF Z-ABSORBING C -ALGEBRAS

By Mikael Rrd Am. 2004

193 citations recorded by the source corpus.

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Citations in the corpus

On the classification problem for nuclear C^*-algebras (2005, background): “e continuous complex-valued functions on a topological space X. 4 ANDREWS.TOMS Let Abe a C∗-algebra. We recall the deﬁnition of the Cuntz semigroup W(A) from [C]. (Our synopsis is essentially that of [R3].) Let Mn(A)+ denote the positive elements of Mn(A), and let M∞(A)+ be the disjoint union ∪∞ i=n”
The Cuntz semigroup as an invariant for C*-algebras (2007, background): “etween the ordered semigroup CuAdeﬁned in Section 1 (and studied in Theorems 1, 2, and 3 and Corollaries 4 and 5 above) and the ordered semigroup introduced by Cuntz in [4]— denoted by WAby Rørdam in [25] and now often called the Cuntz semigroup. (In [25] the structure of WAwas referred to as that o”
Dixmier approximation and symmetric amenability for C*-algebras (2013, background): “o be the counterexamples of Pedersen and Petersen ([PP]), then Q T(An)/U(resp. conv F T(An)) is not weak∗-dense in T( Q An/U) (resp. T( Q An)). The following theorem is proved by Sato [Sa1] (see also [Rø]) in the case where Ais a simple nuclear C∗-algebra having ﬁnitely many extremal tracial states.”
Regularity properties in the classification program for separable amenable C*-algebras (2007, background): “ the (proper) subclass which satisﬁes the original form of the Elliott conjecture (modulo UCT). If one assumes a priori that Ais simple and unital with no tracial state, then a theorem of Rørdam (see [47]) shows that property (ii) above — known as O∞-stability—is equivalent to Z-stability. Under the”
The Rohlin property for automorphisms of the Jiang-Su algebra (2009, background): “orphism δ of Z and a unitary u in Z such that α = Adu◦δ ◦β ◦δ−1. Foraseparable, nuclearC∗-algebraAabsorbingthe Jiang-Sualgebra, Rørdam proved that A is purely inﬁnite if and only if A is traceless in [29], and Nakamura proved that the aperiodicity for automorphisms of purely inﬁnite C∗-algebras coin”
Strict comparison and Z-absorption of nuclear C*-algebras (2011, background): “valent for unital separable simple inﬁnite-dimensional nuclear C∗-algebras (see [21, 26] for example). M. Rørdam proved that Z-absorption implies strict comparison for unital simple exact C∗-algebras [16]. W. Winter showed that any unital separable simple inﬁnite-dimensional C∗-algebra with ﬁnite nu”
The Elliott conjecture for Villadsen algebras of the first type (2006, background): “nﬁnite algebras. The latter states that for a simple, separable, and nuclear C∗-algebra Awe have A⊗O∞ ∼= A⇔ A is purely inﬁnite. If we suppose that Ais a priori traceless, then a result ofRørdam (see [21]) saysthat Z-stability and O∞-stability are equivalent, and the deﬁnition of strict comparison r”
On the Classification of Simple Z‐Stable C*‐Algebras with Real Rank Zero and Finite Decomposition Rank (2005, background): “But now it follows from [16], Theorem 7.”
Decomposition rank of UHF-absorbing c* -algebras (2013, result): “ and strict comparison are equivalent for unital separable simple inﬁnite-dimensional ﬁnite nuclear C∗-algebras (see [33, Conjecture 0.1] for example). The theorem above, together with the results in [13, 27, 33, 20], gives a partial aﬃrmative answer to this conjecture in the following sense. Coroll”
Dimension, comparison, and almost finiteness (2017, background): “ng three conditions are equivalent: 4 DAVIDKERR (i) ﬁnite nuclear dimension, (ii) Z-stability, (iii) strict comparison. The implications (i)⇒(ii) and (ii)⇒(iii) are theorems of Winter [56] and Rørdam [39], respectively. Matui and Sato proved (iii)⇒(ii) when the set of extremal tracial states is ﬁnit”