## 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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