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 -frame is not guaranteed in general. Some characterizations of duals of -frames are given in this paper.
"On duals of $p$-frames." Involve 6 (3) 301 - 309, 2013. https://doi.org/10.2140/involve.2013.6.301