EQUIVALENT CONTINUOUS G-FRAMES IN HILBERT C*-MODULES

In this paper, we investigate the mapping of continuous g-frames in Hilbert C*-module under bounded operators. So, operators that preserve continuous g-frames in Hilbert C*-module were characterized. Then, we introduce equivalent continuous g-frames in Hilbert C*-module by the mapping of continuous g-frames in Hilbert C*-module under bounded operators. We show that every continuous g-frame in Hilbert C*-module is equivalent by a continuous Parseval g-frame in this space. We also verify the relation between the mapping of continuous g-frame in Hilbert C*-module and continuous g-frame operator in Hilbert C*-module. Then, we conclude if two continuous Parseval g-frames in Hilbert C*-module are equivalent then they are unitary equivalent.