Haagerup property for C*-algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:377

Article

Dong, Z.

关键词: Haagerup property;    Relative Haagerup property;    C*-algebra;    Discrete group;    Fourier algebra;   

DOI  :  10.1016/j.jmaa.2010.11.017

来源: Elsevier

【 摘 要 】

We define the Haagerup property for C*-algebras A and extend this to a notion of relative Haagerup property for the inclusion B subset of A. where B is a C*-subalgebra of A. Let Gamma be a discrete group and Lambda a normal subgroup of Gamma, we show that the inclusion A infinity alpha,r Lambda subset of A infinity alpha,r Gamma has the relative Haagerup property if and only if the quotient group Gamma/Lambda has the Haagerup property. In particular, the inclusion C(r)*(Lambda) subset of C(r)*(Gamma) has the relative Haagerup property if and only if Gamma/Lambda has the Haagerup property; C(r)*(Gamma) has the Haagerup property if and only if Gamma has the Haagerup property. We also characterize the Haagerup property for Gamma in terms of its Fourier algebra A(Gamma). (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free