1. Property T for non-unital C*-crossed products.
- Author
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Ng, Chi-Keung and Yao, ZhaoLin
- Subjects
- *
COMPACT groups , *CONTINUOUS functions , *DISCRETE element method - Abstract
Let G be a locally compact group that acts on a C ∗ -algebra A through an action β. Generalizing an existing result for discrete group actions, we show that if there exist a tracial state ϕ on the full crossed product A ⋊ β G and a positive element x 0 in the center of A ⋊ β G with ϕ (x 0) ≠ 0 , then A ⋊ β G has strong property T if and only if G has property T and (A ⋊ β G , A) has strong property T. Furthermore, generalizing another existing result concerning property T for reduced group C ∗ -algebras, we show that if there exist a β-invariant tracial state τ on A and a continuous function f : G → A with compact support such that ∫ G τ (f 2 (s)) d s ≠ 0 , then the reduced crossed product A ⋊ β , r G has strong property T if and only if G has property T and (A ⋊ β , r G , A) has strong property T. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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