Cowling–Haagerup constant of the product of discrete quantum groups

We show that (central) Cowling–Haagerup constant of discrete quantum groups is multiplicative \Lambda_{\mathrm{cb}}(ℾ_{1}\times ℾ_{2})=\Lambda_{\mathrm{cb}}(ℾ_1)\,\Lambda_{\mathrm{cb}}(ℾ_{2}) , which extends the result of Freslon (2015) to general (not necessarily unimodular) discrete quantum groups. The crucial feature of our approach is considering algebras \mathrm{C}(\hat ℾ),\operatorname{L}^{\infty}(\hat ℾ) as operator modules over \operatorname{L}^{1}(\hat ℾ) .