Duality relations associated with weak g-R-duals.

Recently, duality principles in g-frame theory were studied. This paper addresses a relaxation of g-R-duals. We introduce the notion of weak g-R-dual in g-frame theory setting, and present the link between frame properties of a bounded operator sequence and its weak g-R-duals. Using weak g-R-duals, we characterize g-frames and (unitary) equivalence between g-frames. And using pseudo-inverse operators, we represent the canonical duals of weak g-R-duals. Some examples are also provided. [ABSTRACT FROM AUTHOR]