g-标准正交基与g-框架的构造  

Some Properties of g-Orthonormal Basis and g-Frame

作　　者：张艳 张建平 ZHANG Yan;ZHANG Jianping(College of Mathematics and Computer Science,Yan'an University,Yan'an 716000,Shaanxi,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《山西师范大学学报（自然科学版）》2023年第1期1-6,共6页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11961072);陕西省自然科学基础研究计划项目(2020JM-547)。

摘　　要：基于Hilbert空间g-框架理论,借助算子工具,首先对序列成为g-Bessel序列的充分必要条件给出新的证明方法;其次利用Hilbert空间中的g-标准正交基定义g-预框架算子,结合算子论的方法构造新的g-框架、Parseval g-框架、g-Riesz基及g-标准正交基;最后给出两个g-框架成为互补对及强互补对的定义并结合Riesz型g-框架,分别讨论两个g-框架成为互补对及强互补对的充分必要条件.Based on g-frame theory of Hilbert space and operator tool,a new proof method is given for sufficient and necessary conditions for sequences to become g-Bessel sequences.Secondly,g-preframe operator is defined by g-orthonormal basis in Hilbert space,and new g-frame,Parseval g-frame,g-Riesz basis and g-orthonormal basis are constructed by using operator tool method in functional analysis.Finally,the definition of two gframes becoming complementary pair and strong complementary pair is given,and the necessary and sufficient conditions for two g-frames becoming complementary pair and strong complementary pair are discussed respectively.

关 键 词：g-标准正交基 互补对 强互补对 算子论 

分 类 号：O777.1[理学—晶体学]