| 初等算子的正规性 |
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| 引用本文： | 陆芳言.初等算子的正规性[J].应用泛函分析学报,2002,4(2):118-123. |
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| 作者姓名： | 陆芳言 |
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| 作者单位： | 苏州大学数学系,江苏,苏州,215006 |
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| 摘 要： | 设初等算子E（X）＝n↑∑↑i=1AiXBi，定义E^*(X)=n↑∑↑i=1Ai^*XBi^*我们证明了EE^*＝E^*E当县仅当｛Ai｝和｛Bi｝都是交换的正规算子族，从而回答了由D.Keckic提出的关于初等算子正规性的开问题。我们还给出了E＝E^*的充分必要条件。
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| 关 键 词： | 初等算子 正规性 正规算子 |
Normality of Elementary Operators |
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| LU Fang-yan.Normality of Elementary Operators[J].Acta Analysis Functionalis Applicata,2002,4(2):118-123. |
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| Authors: | LU Fang-yan |
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| Abstract: | Given an elementary operator E(X) = AiXBi, we define E* (X) = Ai*XBi*. Inthis note, we prove that EE* = E*E if and only if {Ai} and {Bi} are commuting families of normal perators, which answers the question on normality of elementary operators proposed by D. Keckic. We also give a necessary and sufficient condition that assures that E =E*. |
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| Keywords: | elementary operator normality normal operator |
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