| 本性正规算子的Aluthge变换 |
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| 引用本文： | 张云,陈冬君.本性正规算子的Aluthge变换[J].山东大学学报(理学版),2009,44(3):88-91. |
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| 作者姓名： | 张云 陈冬君 |
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| 作者单位： | 淮北煤炭师范学院数学科学学院,安徽,淮北,235000
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| 基金项目： | 安徽省高校省级自然科学研究项目 |
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| 摘 要： | 设T∈B(H), T=U|T|是算子T的极分解, 则定义Tt=|T|tU|T|1-t和Tt(*)=|T*|tU|T*|1-t(其中0
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| 关 键 词： | 广义Aluthge变换 广义* Aluthge变换 BDF定理 模紧酉等价 |
| 收稿时间： | 2008-09-22 |
Aluthge transforms of essentially normal operators |
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| ZHANG Yun,CHEN Dong-jun.Aluthge transforms of essentially normal operators[J].Journal of Shandong University,2009,44(3):88-91. |
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| Authors: | ZHANG Yun CHEN Dong-jun |
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| Institution: | Department of Mathematics, Huaibei Coal Industry Teachers’ College, Huaibei 235000, Anhui, China |
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| Abstract: | Let T∈B(H), T=U|T| be a polar decomposition of T, then Tt=|T|tU|T|1-t and Tt(*)=|T*|tU|T*|1-t were defined to be the generalized Aluthge transform and the generalized * Aluthge transform of T respectively, t∈(0,1). Using block operator matrices and operator approximation, the relationships among the generalized Aluthge transform, the genralized * Aluthge transform and the class of essentially Normal Operators were discussed. In this note, it was proved that both the generalized Aluthge transform and the generalized * Aluthge transform preserve essential normality. Moreover, it was shown that T, Tt and Tt(*) are mutually essentially unitary equivalent. |
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| Keywords: | the generalized Aluthge transform the genralized *-Aluthge transform BDF theorem compalent |
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