广义Riesz基的双正交特征刻画  

Biorthogonal Characterization of Generalized Riesz Bases

作　　者：张伟 李登峰[2] Wei ZHANG;Deng Feng LI(School of Mathematics and Information Sciences,He'nan University of Economics and Law,Zhengzhou 450046,P.R.China;School of Mathematical&Physical Sciences,Wuhan Textile University,Wuhan 430200,P.R.China)

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450046 [2]武汉纺织大学数理科学学院,武汉430200

出　　处：《数学学报（中文版）》2022年第4期599-606,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(61471410);河南省高等学校重点科研项目(20A110013,21A110004)。

摘　　要：本文利用广义双正交序列研究广义Riesz基的等价刻画,得到了算子序列是广义Riesz基当且仅当该算子列是广义完备的广义Bessel序列,且它存在广义双正交序列及这个双正交序列也是广义完备的广义Bessel序列.进一步证明了等价刻画中两个广义Bessel序列的广义完备性条件可以去掉一个(或者任一个),并举例说明了广义双正交,广义完备与广义Bessel条件之间的关系.In this paper,we investigate the characterization of g-Riesz bases in term of g-biorthogonal sequences.We obtain that a sequence of operators is a g-Riesz basis if and only if it is a g-complete g-Bessel sequence with g-biorthogonal sequence which is also a g-complete g-Bessel sequence,and further prove that the condition for gcompleteness of one(any one) of two g-Bessel sequences can be removed from the characterization.Examples are given to illustrate the relations for g-biorthogonality,g-completeness and g-Bessel condition.

关 键 词：广义Bessel序列 广义Riesz基 广义双正交序列 广义完备 

分 类 号：O174.2[理学—数学]