Integrable actions and transformation groups whose C*-algebras have bounded trace

2002 ◽  
Vol 51 (5) ◽  
pp. 1197-1234 ◽  
Author(s):  
Astrid An Huef
Keyword(s):  
Transformation Groups ◽  
C Algebras ◽  
Bounded Trace

Spectrally bounded traces on C*-algebras

2003 ◽  
Vol 68 (1) ◽  
pp. 169-173 ◽  
Author(s):  
Martin Mathieu
Keyword(s):  
Banach Algebra ◽  
Spectral Radius ◽  
Linear Mapping ◽  
C Algebras ◽  
Spectrally Bounded ◽  
Bounded Trace

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(T x) ≤ Mr(x) for all x ∈ E, where r (·) denotes the spectral radius. We establish the equivalence of the following properties of a unital linear mapping T from a unital C* -algebra A into its centre:(a) T is spectrally bounded;(b) T is a spectrally bounded trace;(c) T is a bounded trace.

Transformation Groups and C ∗ -algebras

1965 ◽  
Vol 81 (1) ◽  
pp. 38 ◽  
Author(s):  
Edward G. Effros
Keyword(s):  
Transformation Groups ◽  
C Algebras

Property T and Amenable Transformation Group C*-algebras

2015 ◽  
Vol 58 (1) ◽  
pp. 110-114 ◽  
Author(s):  
F. Kamalov
Keyword(s):  
Compact Hausdorff Space ◽  
Discrete Group ◽  
Hausdorff Space ◽  
Transformation Group ◽  
Amenable Group ◽  
Transformation Groups ◽  
C Algebra ◽  
C Algebras ◽  
Property T ◽  
Tracial States

AbstractIt is well known that a discrete group that is both amenable and has Kazhdan’s Property T must be finite. In this note we generalize this statement to the case of transformation groups. We show that if G is a discrete amenable group acting on a compact Hausdorff space X, then the transformation group C*-algebra C*(X; G) has Property T if and only if both X and G are finite. Our approach does not rely on the use of tracial states on C*(X; G).

On free transformation groups and C*-algebras

1987 ◽  
Vol 107 (3-4) ◽  
pp. 339-347
Author(s):  
Klaus Thomsen
Keyword(s):  
Transformation Group ◽  
Crossed Product ◽  
Transformation Groups ◽  
Connected Space ◽  
Discrete Transformation ◽  
C Algebras ◽  
The Way

SynopsisWe prove that a free discrete transformation group on a compact connected space X is completely determined by the way C(X) lies inside the corresponding crossed product C*-algebra.

Bounded trace C*-algebras and integrable actions

2005 ◽  
Vol 250 (2) ◽  
pp. 393-410 ◽  
Author(s):  
Robert Archbold ◽  
Klaus Deicke
Keyword(s):  
C Algebras ◽  
Bounded Trace
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