On duals of $p$-frames

Abstract

The concept of frames in a Banach space has been introduced by Gröchenig and developed by several authors. The main feature of a frame is to present every element of the underlying Banach space as a norm-convergent series. In this decomposition, the dual frame plays an essential role. The existence of a dual $p$-frame is not guaranteed in general. Some characterizations of duals of $p$-frames are given in this paper.