正压缩算子Jordan积的最大最小谱点

王月清, 左宁, 杜鸿科

数学学报 ›› 2016, Vol. 59 ›› Issue (3) : 421-432.

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PDF(421 KB)
数学学报 ›› 2016, Vol. 59 ›› Issue (3) : 421-432. DOI: 10.12386/A2016sxxb0041
论文

正压缩算子Jordan积的最大最小谱点

    王月清1, 左宁1,2, 杜鸿科1,2
作者信息 +

Minimum and Maximum Spectrum Points of Jordan Products of Positive Contractions

    Yue Qing WANG1, Ning ZUO1,2, Hong Ke DU1,2
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摘要

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.

Abstract

In this note,the spectrum of Jordan products of positive contractions are discussed.We shall establish characterizations of the minimum and maximum spectrum points of Jordan products of positive contractions.And a characterization of minimum spectral points of Jordan products of orthogonal projections is given.

关键词

正算子 / Jordan积 / 数值域 / / 正交投影

Key words

positive operator / Jordan product / numerical range / spectrum / orthogonal projection

引用本文

导出引用
王月清, 左宁, 杜鸿科. 正压缩算子Jordan积的最大最小谱点. 数学学报, 2016, 59(3): 421-432 https://doi.org/10.12386/A2016sxxb0041
Yue Qing WANG, Ning ZUO, Hong Ke DU. Minimum and Maximum Spectrum Points of Jordan Products of Positive Contractions. Acta Mathematica Sinica, Chinese Series, 2016, 59(3): 421-432 https://doi.org/10.12386/A2016sxxb0041

参考文献

[1] Du H. K., Deng C. Y., Common complements of two subspaces and an answer of Groß's question, Acta Mathematica Sinica, Chinese Series, 2006, 49:1109-1112.
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[3] Klaja H., The numerical range and the spectrum of a product of two orthogonal projections, J. Math. Anal. Appl., 2014, 411:177-195.
[4] Li C. K., Tsai M. C., Wang K. Z., et al., The spectrum of the product of operators, and the product of their numerical ranges, Linear Algebra Appl., 2015, 469:487-499.
[5] Martins E. A., Silva F. C., On the invariant polynomials of Jordan products, Linear Algebra Appl., 2003, 360:173-189.
[6] Martins E. A., Silva F. C., On the eigenvalues of Jordan products, Linear Algebra Appl., 2003, 359:249-262.
[7] Ogasawara T., A theorem on operator algebras, J. Sci. Hiroshima Univ. Ser. A, 1955, 18:307-309.
[8] Stampfli J. D., The norm of a derivation, Pacific J. Math., 1970, 33:737-747.
[9] Wang Y. Q., Du H. K., A characterization of maximum norms of commutators of positive contractions, J. Math. Anal. Appl., 2008, 348:990-995.

基金

国家自然科学基金资助项目(11571211); 重庆科技学院博士教授基金(CK2010B09)

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