| 关于亚正规算子的Hilbert-Schmidt范数不等式 |
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| 引用本文： | 侯晋川.关于亚正规算子的Hilbert-Schmidt范数不等式[J].复旦学报(自然科学版),1988(4). |
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| 作者姓名： | 侯晋川 |
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| 作者单位： | 复旦大学数学研究所 1983级博士研究生 |
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| 摘 要： | 设H为可分无限维Hilbert空间,(T_1,T_2)和(S_1~*,S_2~*)分别为H上重交换的亚正规算子对及次正规算子对,则对任X∈B(H),不等式‖T_1XS_1+T_2XS_2‖_2≥‖T_1~*XS_1~*+T_2~*XS_2~*‖_2都成立;若T,S~*为亚正规算子且‖T‖~2-T~*T为迹类算子,则不等式‖TX-XS‖_2≥‖T~*-XS~*‖_2对任意X∈B(H)都成立。
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| 关 键 词： | Hilbert空间 算子理论 范数 不等式。 |
ON THE HILBERT-SCHMIDT NORM INEQUALITY OF HYPONORMAL OPERATORS |
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| Hou Jinchuan,.ON THE HILBERT-SCHMIDT NORM INEQUALITY OF HYPONORMAL OPERATORS[J].Journal of Fudan University(Natural Science),1988(4). |
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| Authors: | Hou Jinchuan |
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| Institution: | Institute of Mathematics |
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| Abstract: | Let H be a separable infinite-dimensional Hilbert space. If (T_1, T_2) and (S_2~*,S_2~*) are double commuting pairs of hyponormal operators and subnormal operatorson H, respectively, then the inequality (?) holdsfor every bounded linear operator X on H. If T and s~* are hyponormal operatorsand if (?) is of the trace-class, then the inequality (?)holds for every bounded linear operator X. |
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| Keywords: | Hilbertt space operator theory norm inequality |
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