Multiplicativity of the weak Haagerup constant

We prove that the weak Haagerup constant is multiplicative with respect to direct products, namely $Λ_{\mathrm{WH}}(G \times H)=Λ_{\mathrm{WH}}(G) Λ_{\mathrm{WH}}(H)$ for any locally compact groups $G$ and $H$. Knudby previously proved the submultiplicative inequality and asked whether equality alwa