A note on l^p-linear independence and projections of uniqueness

Abstract

We study the problem of l^p-linear independence of orbits of unitary dual integrable representations of countable discrete, not necessarily abelian groups. Under the assumption that the system is Bessel, we prove that for p\in<1, 2> the system is ℓ^p(G)-linearly independent precisely when the projection onto kernel of the corresponding bracket operator is a projection of uniqueness for l^p(G). The existence of such projections for any infinite countable discrete group is guaranteed by the result of Cecchini and Fig\`a- Talamanca.