Parseval p-frames and the Feichtinger conjecture

In this paper, we give a precise characterization of Parseval p-frames by the known Clarlcson's inequality for l(p). As a direct application, we show that every tight p-frame {g(j)}(j=1)(infinity) for l(p), with frame bound B > 0 and inf(j) parallel to g(j)parallel to >= C > 0, can be decomposed into left perpendicularB/C(p)right perpendicular standard q-Riesz basic sequences, and we show that the estimate left perpendicularB/Cpright perpendicular is optimal. Moreover, we prove the existence of a p-frame which is not equivalent to any Parsevel p-frame for l(p), 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 l(q) coefficients for the dual space. (C) 2014 Elsevier Inc. All rights reserved.