Property (Ttt) and the Cowling–Haagerup Constant - Vergara-Soto, I (Birkhauser, 2024)
We show that Property (TTT) is an obstruction to weak amenability with Cowling–Haagerup constant 1. More precisely, if G is a countable group and H is an infinite subgroup of G such that the pair (G, H) has relative Property (TTT), then the weak Haagerup constant ΛWH(G) is strictly greater than 1. We apply this result to some semidirect products and lattices in higher rank algebraic groups. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.