Multiplicativity of the weak Haagerup constant

Abstract

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

arXiv comment14 pages