Equivalency Relations between Continuous g-Frames and Stability of Alternate Duals of Continuous g-Frames in Hilbert C*-Modules

Abstract

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.