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Equivalency relations between continuous g-frames and stability of alternate duals of continuous g-frames in Hilbert \(C^*\)-modules. (English) Zbl 1397.46043

Summary: We introduce the modular continuous g-Riesz basis to improve one existing result for continuous g-Riesz basis in Hilbert \(C^*\)-modules, and then we study the equivalency relations between continuous g-frames in Hilbert \(C^*\)-modules, and, in particular, we obtain two necessary and sufficient conditions under which two continuous g-frames are similar. Finally, we generalize a stability result for alternate duals of g-frames in Hilbert spaces to alternate duals of continuous g-frames in Hilbert \(C^*\)-modules.

MSC:

46L08 \(C^*\)-modules
42C15 General harmonic expansions, frames
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