Continuous G-Frames In Hilbert Spaces

This paper mainly discusses Continuous g-frames' basic properties and some generaliza-tions.The article includes three chapters:In chapter one,we introduce the emergence and development of frame theory in the sepa-rable Hilbert space,the main work of this paper and the preparatory knowledge to be used.In chapter two,we introduce the concept of approximation dual continuous g-frame and discuss its properties.Firstly,we generalize some equations and inequalities of g-frames to continuous g-frames in Hilbert spaces,and obtain different forms of equality and inequality.Secondly,the concept of continuous g-dual frame is introduced,and its properties are studied.Finally,the simple structure of continuous g-dual frame is given.In chapter three,firstly,we generalize the continuous K-frame and its properties,and obtain some basic conclusions of the continuous g-K-frame.secondly,we introduce the concept of locally continuous g-frame.The relation between continuous g-K-frame and locally continuous g-frame is discussed.Finally,the stability of continuous g-K-frame is studied by means of operator theory,and some new results are obtained.