Generalized G-frames In Hilbert C~*-modules

This thesis is devoted to generalizing generalized g-frame to the Hilbert C~*-module setting . Introduce the notions of generalized g-frame, generalized tight g-frame, generalized normalized tight g-frame generalized canonical dual g-frame and generalized alternate dual g-frame in Hilbert C~*-modules.In this thesis, some definitions such as generalized g-analysis operator, generalized g-frame operator and generalized g-dual frame for a given generalized g-frame are introduced, and the reconstruction formula which is very important in frame theory is available.The strong disjointness, disjointness and weak disjointness in Hilbert C~*-module are studied, and we connected them with the range of the generalized g-analysis operator.Some perturbation conditions about generalized g-frames, accompanying with the new bounds under perturbations and some other useful results, are intensively investigated.At the end of this thesis, the equalities and inequalities about Hilbert C~*-modular frames, especially the generalized g-Parseval frame equality are studied.