Uniformly bounded representations and completely bounded multipliers of SL(2,R)

TL;DR

This paper investigates the norms of matrix coefficients of irreducible uniformly bounded representations of SL(2,R), revealing potential improvements in the known inequalities relating these norms.

Contribution

It provides new estimates for the norms of matrix coefficients, challenging the optimality of existing inequalities between uniformly bounded and completely bounded norms.

Findings

Norm estimates suggest the known inequalities may not be optimal

Many matrix coefficients are shown to be completely bounded multipliers

Results impact understanding of representation theory of SL(2,R)

Abstract

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, 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.