摘要
考虑了g-框架的一些新性质.首先把有关框架的投影方法推广到g-框架,并且建立了一个类似的该方法对g-框架有效的充分必要条件.然后研究了包含g-Riesz基的g-框架,得到了在某些条件下g-Riesz框架一定包含g-Riesz基.我们提出了具有子g-框架性质的g-框架的概念,证明了在某些条件下具有子g-框架性质的g-框架一定包含一个g-Riesz基.最后得到了一些g-框架与其诱导出的框架之间的在某些限制条件下的等价性质.
In this paper,some properties of g-frames are considered.Firstly,we generalize the projection methods for frames to g-frames and a similar if and only if condition for such method works is established.Then we study the g-frames which contain g-Riesz bases.We obtain that under some constraint g-Riesz frame contains a g-Riesz basis.We also introduce the conception of g-frames with sub-g-frame property and show that under some restriction g-frame with sub-g-frame property contains a gRiesz basis.Finally,we get several equivalent properties between g-frames and frames induced by the g-frames under some assumptions.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2014年第5期881-892,共12页
Acta Mathematica Sinica：Chinese Series
