Hilbert C*模上的广义g框架的扰动

Perturbations of Generalized gframe in Hilbert C*modules

摘要:

主要研究了Hilbert C*模上的广义g框架在扰动条件下的稳定性，即一族元素与给定的广义g框架满足什么条件时能构成广义g框架.类似于Hilbert空间中的情形，具体给出了3类不同的扰动条件，并用算子理论的方法和技巧证明了广义g框架在这3类扰动下的不变性结论.最后讨论了Hilbert C*模上的广义对偶g框架的稳定性的结果.

关键词:Hilbert C*模; 广义g框架; 广义g框架算子; 扰动

Abstract:

The stability of the Hilbert C* modular generalized g frames under some perturbations was studied to see whether the family will become a generalized g frame under some perturbations related to the fixed frame. Similar to the Hilbert space, three different situations and respective conclusions were proposed, which were proved by using operator theoretic methods. Besides, the stability of the generalized dual g frame was discussed.

Key words:Hilbert C*module; generalized gframe; generalized gframe operators; perturbation