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In this paper we give some new results for g-frames in Hilbert C * -modules and then we introduce a bounded A-linear operator L, by means of this operator L we character the properties of the g-frames and g-Riesz basis in Hilbert C * -modules. Finally, we establish some important equalities and inequalities for frames and g-frames in Hilbert C * -modules.

In this paper, we derive some equalities and inequalities about g-continuous frames, which are an extension to g-frames and continuous frames We also discuss the stability of the perturbation of a g-continuous frameNational Natural Science Foundation of China [10571145]; Natural Science Foundation of Fujian Province of China [2010J01012]; Science and Technology Foundation of Xiamen City of China [20083012

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The concept of g-frame and g-Riesz basis in a complex Hilbert space was introduced by Sun. 18 In this paper, we generalize the g-frame and g-Riesz basis in a complex Hilbert space to a complex Banach space. Using operators theory and methods of functional analysis, we give some characterizations of a g-frame or a g-Riesz basis in a complex Banach space. We also give a result about the stability of g-frame in a complex Banach space.