E-resources
Peer reviewed
-
BANNON, JON P.; FANG, JUNSHENG
Journal of operator theory, 03/2011, Volume: 65, Issue: 2Journal Article
A finite von Neumann algebra 𝓜 with a faithful normal trace τ has Haagerup's approximation property if there exists a pointwise deformation of the identity in 2-norm by subtracial compact completely positive maps. In this paper we prove that the subtraciality condition can be removed. This enables us to provide a description of Haagerup's approximation property in terms of correspondences. We also show that if 𝓝 ⊂ 𝓜 is an amenable inclusion of finite von Neumann algebras and 𝓝 has Haagerup's approximation property, then 𝓜 also has Haagerup's approximation property.
