OPERATOR THEORY AND CONTINUOUS G-FRAME IN HILBERT MODULE

The authors generalize g-frame in Hilbert C*- modules. This generalization is a natural generalization of continuous and discrete g-frame and frame in Hilbert space too. In this paper, by considering operator theoretic property in Hilbert C*-module, continuous g-frames in Hilbert C*-module are verified. In particular, by defining an operator L on g- Bessel nets, the authors investigate the situations in which the operator L preserves the g-frame property