Fixed-points in the cone of traces on a C*-algebra
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Fixed-points in the cone of traces on a C*-algebra. / Rørdam, Mikael.
In: Transactions of the American Mathematical Society, Vol. 371, No. 12, 2019, p. 8879-8906.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Fixed-points in the cone of traces on a C*-algebra
AU - Rørdam, Mikael
PY - 2019
Y1 - 2019
N2 - Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a nonzero fixed-point when acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod’s results say about the existence of invariant traces on (typically nonunital) C*-algebras equipped with an action of a group with the fixed-point property for cones. As an application of these results, we provide results on the existence (and nonexistence) of traces on the (nonuniform) Roe algebra.
AB - Nicolas Monod introduced the class of groups with the fixed-point property for cones, characterized by always admitting a nonzero fixed-point when acting (suitably) on proper weakly complete cones. He proved that his class of groups contains the class of groups with subexponential growth and is contained in the class of supramenable groups. In this paper we investigate what Monod’s results say about the existence of invariant traces on (typically nonunital) C*-algebras equipped with an action of a group with the fixed-point property for cones. As an application of these results, we provide results on the existence (and nonexistence) of traces on the (nonuniform) Roe algebra.
UR - http://www.scopus.com/inward/record.url?scp=85070268517&partnerID=8YFLogxK
U2 - 10.1090/tran/7797
DO - 10.1090/tran/7797
M3 - Journal article
AN - SCOPUS:85070268517
VL - 371
SP - 8879
EP - 8906
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 12
ER -
ID: 226948274