广义框架的不相交性

Disjointness of Generalized Frames

Hilbert空间中框架的不相交性是由Han和Larson首先提出的,它与超框架有着密切的联系,在超框架及框架的构造中扮演重要的角色.广义框架是通常框架的推广.该文利用超广义框架刻画了广义框架的不相交性、强不相交性及弱不相交性;借助所得结果,给出了已知定理的不同证明方法;建立了对偶广义框架之间强不相交相和弱不相交性之间的关系;最后利用给定的强不相交的广义框架构造新的(超)对偶广义框架,所得结论恢复已有结果.

The notion of disjointness of frames in Hilbert spaces was firstly introduced by Han and Larson,it is closely related with super frames in Hilbert spaces,and plays an important role in construction of super frames and frames.G-frames is a generalization of frames in Hilbert spaces.In this paper,we establish characterization of disjointness of g-frames,strong disjointness of g-frames and weak disjointness of g-frames in terms of super g-frames;With the results obtained,we give different proof method of the known theorem;We obtain the relation between strongly disjoint and weakly disjoint of dual g-frames;Finally,we use strong disjointness of g-frames to construct(super)dual g-frames,which cover the results obtained by other authors.