Hilbert空间中K-g-框架的性质及扰动

Properties and Perturbations of K-g-frames in Hilbert Space

Hilbert空间中的K-g-框架作为g-框架的一种特殊推广,是周燕(2014)在研究g-框架的性质及扰动时提出的.在已有文献的基础上,改变了原有条件和框架中元素的域,给出了Hilbert空间中K-g-框架的一个充分条件和一个必要条件,然后得到了一个框架界为‖T‖^(-2)‖K‖^(-2)和B的K-g-框架的充要条件.最后证明了K-g-框架在简化后的扰动条件下的稳定性.

The K-g-frame,which is a generalization of a g-frame in a Hilbert space,was introduced by Zhou Yan to study properties and perturbations of g-frame.Based on the existing papers,the original conditions and the domain of elements in the frame are changed.This paper gives a sufficient condition and a necessary condition of K-g-frame in Hilbert space,then we obtain a necessary and sufficient condition for a K-g-frame whose frame bounds are‖T‖^(-2)‖K‖^(-2)and B.Finally,the stability of K-g-frame under simplified perturbation conditions is proved.