Original scientific paper

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

Ivana Slamić orcid.org/0000-0002-3284-8052 ; Faculty of Mathematics, University of Rijeka, Rijeka, Croatia

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.

Keywords

l^p-linear independence; dual integrable representation; bracket; projection of uniqueness

Hrčak ID:

309004

URI

https://hrcak.srce.hr/309004

Publication date:

22.10.2023.

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