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THE SCHUR TEST OF COMPACT OPERATORS
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作者 qijian kang Maofa WANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期2041-2050,共10页
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 t... 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). 展开更多
关键词 Schur test compact operator infinite matrix
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