Characteizations of woven g-frames and weaving g-frames in Hilbert spaces and C*-modules

Abstract

In this paper, using Parseval frames we generalize Sun’s results to g-frames in Hilbert C*-modules. Moreover, for g-frames in Hilbert spaces, we present some characterizations in terms of a family of frames, not only for orthonormal bases. Also, we have a note about a comment and a relation in the proof of Proposition 5.3 in [D. Li et al., On weaving g-frames for Hilbert spaces, Complex Analysis and Operator Theory, 2020]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.