Boundary rigidity for free product C∗-algebras
نویسندگان
چکیده
منابع مشابه
Projections in Free Product C {algebras
Consider the reduced free product of C {algebras, (A; ') = (A 1 ; ' 1) (A 2 ; ' 2), with respect to states ' 1 and ' 2 that are faithful. If ' 1 and ' 2 are traces, if the so{called Avitzour conditions are satissed, (i.e. A 1 and A 2 are not \too small" in a speciic sense) and if A 1 and A 2 are nuclear, then it is shown that the positive cone, K 0 (A) + , of the K 0 {group of A consists of tho...
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Let (A; ') be the reduced free product of innnitely many C {algebras (A ; ') with respect to faithful states. Assume that the A are not too small, in a speciic sense. If ' is a trace then the positive cone of K 0 (A) is determined entirely by K 0 ('). If, furthermore, the image of K 0 (') is dense in R, then A has real rank zero. On the other hand, if ' is not a trace then A is simple and purel...
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Let l be a length function on a group G, and let Ml denote the operator of pointwise multiplication by l on l(G). Following Connes, Ml can be used as a “Dirac” operator for C ∗ r (G). It defines a Lipschitz seminorm on C∗ r (G), which defines a metric on the state space of C∗ r (G). We show that if G is a hyperbolic group and if l is a word-length function on G, then the topology from this metr...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2018
ISSN: 0024-6093
DOI: 10.1112/blms.12180