A Hilbert Module Approach to the Haagerup Property

作者：Dong Zhe; Ruan Zhong Jin^*

来源：Integral Equations and Operator Theory, 2012, 73(3): 431-454.

DOI：10.1007/s00020-012-1979-3

• Hilbert modules
• multipliers
• Haagerup property
• coarse embedding
• exact groups

We develop a Hilbert module version of the Haagerup property for general C*-algebras . We show that if is an action of a countable discrete group I" on a unital C*-algebra , then the reduced C*-algebra crossed product has the Hilbert -module Haagerup property if and only if the action alpha has the Haagerup property. We are particularly interested in the case when is a unital commutative C*-algebra. We compare the Haagerup property of such an action with the two special cases when (1) I" has the Haagerup property and (2) I" is coarsely embeddable into a Hilbert space. We also prove a contractive Schur mutiplier characterization for groups coarsely embeddable into a Hilbert space, and a uniformly bounded Schur multiplier characterization for exact groups.

• 出版日期2012-7
• 单位浙江大学