On the paper "Characterizations of weaving for $g$-frames by induced sequences"

TL;DR

This paper clarifies inaccuracies in previous works on weaving g-frames, correcting a counter-example and addressing misinterpretations, thereby refining the theoretical understanding of g-frames in Hilbert spaces.

Contribution

It identifies and corrects errors in prior characterizations of weaving g-frames, providing clearer insights into their properties.

Findings

Counter-example in previous work is incorrect

No new characterization of weaving g-frames was introduced

Existing characterizations are reaffirmed as correct

Abstract

A counter-example by Xiangchun Xiao, Guoping Zhao and Guorong Zhou in [J. Pseudo-Differ. Oper. Appl., (2021) 12:60] is incorrect. Further, there is no new characterization of weaving for g-frames by Xiangchun Xiao et al. in [2]. Xiangchun Xiao et al. in [2] gave a wrong interpretation about a characterization of weaving g-frames in separable Hilbert spaces which already proved by Deepshikha, Vashisht and Verma in [1].