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Generalization of the Lieb–Thirring–Araki Inequality and Its Applications

Author

Listed:
  • Yonggang Li

    (College of Science, Zhengzhou University of Aeronautics, Zhengzhou 450015, China)

  • Jing Wang

    (School of Information, Beijing Wuzi University, Beijing 101149, China)

  • Huafei Sun

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

The matrix eigenvalue is very important in matrix analysis, and it has been applied to matrix trace inequalities, such as the Lieb–Thirring–Araki theorem and Thompson–Golden theorem. In this manuscript, we obtain a matrix eigenvalue inequality by using the Stein–Hirschman operator interpolation inequality; then, according to the properties of exterior algebra and the Schur-convex function, we provide a new proof for the generalization of the Lieb–Thirring–Araki theorem and Furuta theorem.

Suggested Citation

  • Yonggang Li & Jing Wang & Huafei Sun, 2021. "Generalization of the Lieb–Thirring–Araki Inequality and Its Applications," Mathematics, MDPI, vol. 9(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:723-:d:524903
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