Parseval p-frames and the Feichtinger conjecture


In this paper, we give a precise characterization of Parseval p-frames by the known Clarkson's inequality for ℓp. As a direct application, we show that every tight p-frame {gj}j=1∞ for ℓp, with frame bound B>0 and infj{norm of matrix}gj{norm of matrix}≥C>0, can be decomposed into ⌊B/Cp⌊ standard q-Riesz basic sequences, and we show that the estimate ⌊B/Cp⌊ is optimal. Moreover, we prove the existence of a p-frame which is not equivalent to any Parsevel p-frame for ℓp, and a Parseval p-frame which is not a Schauder frame sequence for the space or its dual space, while we obtain that every p-frame can become a pseudo-framing with ℓq coefficients for the dual space.

Publication Title

Journal of Mathematical Analysis and Applications