Some properties of g-frames in Hilbert \(C^{*}\)-modules (Q1046493)

\textit{W.-C.\thinspace Sun} [``g-frames and g-Riesz bases'', J.~Math.\ Anal.\ Appl.\ 322, No.\,1, 437--452 (2006; Zbl 1129.42017)] introduced the notion of g-frame in Hilbert spaces that extends the notion of frame and investigated some properties of g-frames. In this paper, the authors give an operator-theoretic characterization of g-frames in Hilbert \(C^*\)-modules and prove some equalities and inequalities of frames and g-frames in Hilbert \(C^*\)-modules. Unfortunately, there are some mistakes in the proof of Theorems 3.3 and 3.4, and some statements are ambiguous.