THE SCHUR TEST OF COMPACT OPERATORS  

作　　者：Qijian KANG Maofa WANG 康齐健;王茂发(School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang,524048,China;School of Mathematics and Statistics,Wuhan University,Wuhan,430072,China)

机构地区：[1]School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang,524048,China [2]School of Mathematics and Statistics,Wuhan University,Wuhan,430072,China

出　　处：《Acta Mathematica Scientia》2024年第5期2041-2050,共10页数学物理学报（B辑英文版）

基　　金：supported by NSFC(12171373).

摘　　要：Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).

关 键 词：Schur test compact operator infinite matrix 

分 类 号：O177[理学—数学]