HERZ–SCHUR MULTIPLIERS AND NON-UNIFORMLY BOUNDEDREPRESENTATIONS OF LOCALLY COMPACT GROUPS
Troels Steenstrup
Abstract: Let be a second countable, locally compact group and let be a continuous
Herz–Schur multiplier on . Our main result gives the existence of a (not necessarily
uniformly bounded) strongly continuous representation of on a Hilbert space ,
together with vectors , such that for
and . Moreover, we obtain control
over the growth of the representation in the sense that for ,
where is the identity element, is a constant, and is a metric on .