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The spectrum of the product of operators, and the product of their numerical ranges

Chi-Kwong Li Ming-Cheng Tsai Kuo-Zhong Wang Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43670

Linear Algebra and its Applications, 469, 487-499, 2015.3
We show that a compact operator A is a multiple of a positive semi-definite operator if and only if (A B) W (A) W (B), for all (rank one) operators B. An example of a normal operator is given to show that the equivalence conditions may fail in general. We then obtain conditions to identify other classes of operators A so that equivalence conditions hold.
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@inproceedings{chi-kwong2015the,
  title={The spectrum of the product of operators, and the product of their numerical ranges},
  author={Chi-Kwong Li, Ming-Cheng Tsai, Kuo-Zhong Wang, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210142554097199},
  booktitle={Linear Algebra and its Applications},
  volume={469},
  pages={487-499},
  year={2015},
}
Chi-Kwong Li, Ming-Cheng Tsai, Kuo-Zhong Wang, and Ngai-Ching Wong. The spectrum of the product of operators, and the product of their numerical ranges. 2015. Vol. 469. In Linear Algebra and its Applications. pp.487-499. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020210142554097199.
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