Characterizations of woven g-frames and weaving g-frames in Hilbert spaces and \(C^\ast\)-modules. (Characteizations of woven g-frames and weaving g-frames in Hilbert spaces and \(C^\ast\)-modules.) (English) Zbl 1538.46079
Summary: In this paper, using Parseval frames we generalize Sun’s results to g-frames in Hilbert \(C^\ast\)-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.-W. Li et al., Complex Anal. Oper. Theory 14, No. 2, Paper No. 33, 25 p. (2020; Zbl 1436.42037)]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.
MSC:
| 46L08 | \(C^*\)-modules |
| 42C15 | General harmonic expansions, frames |
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
Citations:
Zbl 1436.42037References:
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