On the Haagerup Property of C^(*)-Dynamical Systems  

作　　者：Changyuan GAO Qing MENG 

机构地区：[1]School of Mathematical Sciences,Qufu Normal University,Shandong 273165,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2022年第6期628-636,共9页数学研究及应用（英文版）

基　　金：the Natural Science Foundation of Shandong Province (Grant No. ZR2020MA008);the China Postdoctoral Science Foundation (Grant No. 2018M642633)

摘　　要：Let A be a unital C^(*)-algebra with a state τ and G be a discrete group that acts on A through a τ-preserving action α. We first generalize the Haagerup property of dynamical systems by considering states and prove that the dynamical system has the Haagerup property if and only if the reduced crossed product does. Then we introduce the quasi-amenable action of G on A with respect to τ. Finally, using the above results, we prove that if α is a quasiamenable action of G on A with respect to τ, then(A, τ) has the Haagerup property if and only if(A ■α,r G, τ′) does, where τ′is the induced state on A ■α,r G. As a consequence, our main results improve some well known results in the classical situation.

关 键 词：C*-dynamical system Haagerup property quasi-amenable action 

分 类 号：O19[理学—数学]