摘要
g-框架作为Hilbert空间中的推广框架最近被提出,它们有许多和框架类似的性质,但并不是所有的性质都是相似的.Christensen已指出了每个Riesz框架都包含一个Riesz基.本文指出并不是所有的g-Riesz框架都包含一个g-Riesz基,但我们得到了每个g-Riesz框架都包含一个无冗g-框架,同时给出了Hilbert空间中的g-Riesz框架的一个充分必要条件,由此可以得到Riesz框架的刻画.最后讨论Hilbert空间中的g-Riesz框架在扰动下的稳定性.g-Riesz框架的这些性质与Riesz框架的性质并不是一样的.
G-frames, which were proposed recently as generalized frames in Hilbert spaces, share many similar properties with frames, but not all the properties of them are similar. Christensen presented that every Riesz frame contains a Riesz basis. In this paper, the authors showed that not all g-Riesz frames contain a g-Riesz basis, but they obtained that every g-Riesz frame contains an exact g-frame. They also gave a necessary and sumcient condition for a g-Riesz frame in a Hilbert space. Prom this, they might get the characterization of Riesz frames. Lastly the authors considered the stability of a g-Riesz frame for a Hilbert space under perturbations. These properties of g-Riesz frames in Hilbert spaces are not similar to those of Riesz frames.
出处
《中国科学：数学》
CSCD
北大核心
2011年第1期53-68,共16页
Scientia Sinica：Mathematica
基金
福建省自然科学基金(批准号:2009J01007)
福建省教育厅基金(批准号:JA08013)资助项目
