Amenability properties of the centres of group algebras

Abstract

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups. We also, study, for some non-compact groups G, some conditions which imply amenability and hyper-Tauberian property, for ZL1(G).

20 pages

References in corpus (2)

• Convolutions on compact groups and Fourier algebras of coset spaces
• Hypergroups with Unique Alpha-Means

Cited by in corpus (1)

• Weak amenability of Fourier algebras on compact groups