The Stability Of Some Frames In Hilbert Spaces

By using the method of operator theory,the properties and stability of some frames in Hilbert spaces are discussed in this work,and the relevant contents of literatures are supple-mented and extended.The full text is divided into four chapters,the structure and content of specific articles are as follows:Chapter I:Introduction.The development of frame theory in Hilbert spaces are summarized and the main work of this paper is outlined;Chapter II:Preparatory knowledge.This chapter first introduces the concept of frame,K-frame and generalized frame in Hilbert spaces,and their properties and stability are studied and discussed;Chapter III:The stability of the discrete frame.By using the related concepts of frame theory,functional analysis,the method of the operator theory,the stability of dual frame,the K-frame vector for unitary system and K-fusion frame are discussed in Hilbert spaces,and the related conclusions in the literatures are improved and optimized;Chapter IV:The stability of the generalized frame.In this chapter,the concepts of the pair of generalized frame,the generalized K-duality,and the generalized K-dual pair are introduced.By using the method of operator theory,the stability of the pair of generalized frame,the sum of generalized frame and the generalized K-dual are discussed,respectively.