We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of $\mathrm {SL}(2,\mathbb{R})$ as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal.
Adv. Oper. Theory
3(1):
247-270
(Winter 2018).
DOI: 10.22034/aot.1707-1207
