| U-标算子的结构分析 |
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| 引用本文： | 孙万贵.U-标算子的结构分析[J].数学学报,2006,49(2):465-468. |
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| 作者姓名： | 孙万贵 |
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| 作者单位： | 西北大学经济管理学院,西安710069 |
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| 基金项目： | 国家自然科学基金资助项目（10271097） |
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| 摘 要： | 类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”．尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立．本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件．
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| 关 键 词： | U-标算子 Hermite算子 标型谱算子 |
| 文章编号： | 0583-1431（2006）02-0465-04 |
| 收稿时间： | 2005-02-04 |
| 修稿时间： | 2005-02-042005-04-07 |
The Structural Analysis of U-Scalar Operators |
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| Wan Gui SUN.The Structural Analysis of U-Scalar Operators[J].Acta Mathematica Sinica,2006,49(2):465-468. |
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| Authors: | Wan Gui SUN |
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| Institution: | Wan Gui SUN School of Economics & Management, Northwest University, Xi'an 710069, P. R. China |
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| Abstract: | Whether a U-scalar operator is a quasi-affine transform of a self-adjoint operator, similar to a spectral operator of scalar type, is an open question. Although it holds true for the U-scalar operator with purely discrete spectrum, the question, generally speaking, is negative. The aim of this paper is to address this problem. It is proved that a U-scalar operator in a Hilbert space is a Hermitian operator in the sense of a strong-norm topology, and the necessary and sufficient conditions are given under which a U-scalar operator is a spectral operator of scalar type. |
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| Keywords: | U-scalar operator Hermitian oDerator sDectral operator of scalar tvne |
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