本文引入并研究了Banach空间中的X_d框架,X_d Bessel列,紧X_d框架,独立X_d框架和X_d Riesz基等概念,给出了X_d框架和独立X_d框架的算子等价刻画,Banach空间X中存在X_d框架或X_d Riesz基的充要条件以及X_d框架的对偶框架存在的充要条件,讨论了Banach空间的基和X_d框架,X_d Riesz基之间的关系．

In this paper,we introduce and discuss X_d frames,X_d Bessel sequences, tight X_d frames,independent X_d frames and X_d Riesz basis for a Banach space.We give a necessary and sufficent condition for a Banach space X to have an X_d frame or to have an X_d Riesz basis,and a necessary and sufficent condition for an X_d frame to have a dual frame.We also discuss some relations among basis,X_d frame and X_d Riesz basis in a Banach space.