Hilbert空间中的fusion-Besselian框架与拟fusion-Riesz基  

Fusion-Besselian Frames and Fusion-Riesz Bases in Hilbert Spaces

作　　者：王亚玲 杨洪军 王靖华[2] WANG Yaling;YANG Hongjun;WANG Jinghua(Manzhouli Russian Vocational College,Manzhouli 021400,China;Aviation University of Air Force,Changchun 130022,China)

机构地区：[1]满洲里俄语职业学院,内蒙古满洲里021400 [2]空军航空大学基础部

出　　处：《通化师范学院学报》2024年第6期8-16,共9页Journal of Tonghua Normal University

基　　金：内蒙古自治区教育科学研究“十三五”规划课题(NZJGH2020105);内蒙古哲学社会科学规划项目(2017NDC133)。

摘　　要：fusion框架作为Hilbert空间中g-框架的特例,与g-框架有许多类似的性质.该文在已有文献的基础上,借助算子理论知识,举反例说明去掉有限维空间的条件下结论不成立,进一步给出fusion-Besselian框架的算子刻画.结合fusion-Besselian框架的算子刻画和反例1,阐明在探讨该类框架性质时,应关注其适用条件和范围.随后讨论拟fusion-Riesz基与拟Riesz基、fusion-Besselian框架之间的关系.最后讨论fusion-Besselian框架和拟fusion-Riesz基的算子扰动,所得结论补充了算子扰动方面的研究.Fusion-frames,which are special cases of g-frames in Hilbert space,share many similar prop⁃erties with g-frames,but it does not mean that all properties are similar.On the basis of the existing research,this paper uses the operator theory to discuss the equivalent characterization of fusion-Besselian frames,and a counter example is given to show that the conclusion is not valid without the finite dimen⁃sion space.Furthermore,the operator characterization of fusion-Besselian frames is given.Combining the operator characterization of fusion-Besselian frames with the first counter example,it is shown that the conditions and scope of application should be concerned.Then we discuss the relations among near fusion-Riesz bases,near Riesz bases and fusion-Besselian frames.Finally,the operator perturbations of the fusion-Besselian frames and the near fusion-Riesz bases are discussed,supplementing the research on operator perturbations.

关 键 词：G-框架 fusion框架 fusion-Besselian框架 拟fusion-Riesz基 

分 类 号：O177.1[理学—数学]