Completely bounded lacunary sets for compact non-abelian groups
In this paper, we introduce and study the notion of completely bounded sets ( for short) for compact, non-abelian groups G. We characterize sets in terms of completely bounded multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are sets for all p < ∞, but are not for any p ≥ 4. This is done by showing that the space of completely bounded multipliers...