Stability of the weak Haagerup property under graph products

Abstract

In this paper we prove that: Any graph product of finitely many groups, all of them satisfying weak Haagerup property with $\Lambda_{WH}=1$, also satisfies weak Haagerup property and as a corollary of this result we obtain that the free product of weakly Haagerup groups with $\Lambda_{WH}=1$, again has weak Haagerup property with $\Lambda_{WH}=1$.