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More Generalizations of Hartfiel’s Inequality and the Brunn–Minkowski Inequality

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Abstract

In this note, we give some other generalizations of Hartfiel’s inequality and the Brunn–Minkowski inequality to sector matrices, the results obtained improve those of Lin (Arch Math 104:93–100, 2015) and Liu (Linear Algebra Appl 508:206–213, 2016).

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References

  1. Drury, S., Lin, M.: Singular value inequalities for matrices with numerical ranges in a sector. Oper. Matrices 8, 1143–1148 (2014)

    Article  MathSciNet  Google Scholar 

  2. Fan, K.: Some inequalities concerning positive-definite Hermitian matrices. Proc. Camb. Philos. Soc. 51, 414–421 (1955)

    Article  MathSciNet  Google Scholar 

  3. George, A., Ikramov, K.H.D.: On the properties of accretive–dissipative matrices. Math. Notes 77, 767–776 (2005)

    Article  MathSciNet  Google Scholar 

  4. Hartfiel, D.J.: An extension of Haynsworth’s determinant inequality. Proc. Amer. Math. Soc. 41, 463–465 (1973)

    MathSciNet  MATH  Google Scholar 

  5. Haynsworth, E.V.: Applications of an inequality for the Schur complement. Proc. Amer. Math. Soc. 21, 512–516 (1970)

    Article  MathSciNet  Google Scholar 

  6. Hou, L., Dong, S.: An extension of Hartfiel’s determinant inequality. Math. Inequal. Appl. 21, 1105–1110 (2018)

    MathSciNet  MATH  Google Scholar 

  7. Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)

    MATH  Google Scholar 

  8. Ikramov, K.H.D.: Determinantal inequalities for accretive–dissipative matrices. J. Math. Sci. 121, 2458–2464 (2004)

    Article  MathSciNet  Google Scholar 

  9. Lin, M.: Fischer type determinantal inequalities for accretive–dissipative matrices. Linear Algebra Appl. 438, 2808–2812 (2013)

    Article  MathSciNet  Google Scholar 

  10. Lin, M.: Extension of a result of Hanynsworth and Hartfiel. Arch. Math. 104, 93–100 (2015)

    Article  Google Scholar 

  11. Lin, M.: Some inequalities for sector matrices. Oper. Matrices 10, 915–921 (2016)

    Article  MathSciNet  Google Scholar 

  12. Lin, M., Zhou, D.: Norm inequalities for accretive–dissipative operator matrices. J. Math. Anal. Appl. 407, 436–442 (2013)

    Article  MathSciNet  Google Scholar 

  13. Liu, J.: Generalizations of the Brunn–Minkowski inequality. Linear Algebra Appl. 508, 206–213 (2016)

    Article  MathSciNet  Google Scholar 

  14. Yuan, J., Leng, G.: A generalization of the matrix form of the Brunn–Minkowski inequality. J. Aust. Math. Soc. 83, 125–134 (2007)

    Article  MathSciNet  Google Scholar 

  15. Zhang, D., Hou, L., Ma, L.: Properties of matrices with numerical ranges in a sector. Bull. Iran. Math. Soc. 43, 1699–1707 (2017)

    MathSciNet  MATH  Google Scholar 

  16. Zheng, Y., Jiang, X., Chen, X., Alsaadi, F.: More extensions of a determinant inequality of Hartfiel. Linear Algebra Appl. 369, 124827 (2020)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We acknowledge the helpful comments from the referee. The work was supported by National Natural Science Foundation of China (NNSFC) [Grant number 11971294].

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Authors and Affiliations

  1. College of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China

    Sheng Dong

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Qing-Wen Wang

Authors
  1. Sheng Dong
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  2. Qing-Wen Wang
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Correspondence to Sheng Dong.

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Communicated by Abbas Salemi.

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Dong, S., Wang, QW. More Generalizations of Hartfiel’s Inequality and the Brunn–Minkowski Inequality. Bull. Iran. Math. Soc. 47, 21–29 (2021). https://doi.org/10.1007/s41980-020-00363-z

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  • DOI: https://doi.org/10.1007/s41980-020-00363-z

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