Skip to main content
SpringerLink
Log in

On the Origin and Numerical Range of Bounded Operators

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chen, M., Yeh, L.: On the boundary of the numerical range of a matrix. Appl. Math. Lett., 23, 725–727 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Embry, M. R.: The numerical range of an operator. Pacific Journal of Mathematics, 30, 647–650 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goldstein, J. A.: Semigroup of Linear Operator and Application, Oxford University Press, New York, 1985

    Google Scholar 

  4. Hausdorff, F.: Der Wertvorrat einer Bilinearform. Math. Z., 3, 314–316 (1913)

    Article  MathSciNet  MATH  Google Scholar 

  5. Philipp, F., Trunk, C.: The numerical range of non-negative operators in Krein space. Linear Algebra Appl., 15, 1–17 (2012)

    Google Scholar 

  6. Psarrakos, P. J., Tsatsomeros, M. J.: Numerical Range: (in) a Matrix Nutshell, Washihgton State University, Seattle, 2003

    Google Scholar 

  7. Wu, D. Y., Alatancang: Spectral Theory of Block Operator Matrices and Applications, Science Press, Beijing, 2013 (in Chinese)

    Google Scholar 

  8. Zhang, H., Dou, Y., Wang, M., et al.: On the boundary of the numerical range of operators. Appl. Math. Lett., 24, 620–622 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Thank to the referees for several remarks and carefully review of this paper, especially on Theorem 2.8.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, P. R. China

    Xiao Hong Wu & Jun Jie Huang

  2. Department of Mathematics, Hohhot Minzu College, Hohhot, 010051, P. R. China

    Xiao Hong Wu &  Alatancang

Authors
  1. Xiao Hong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Jie Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alatancang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Jie Huang.

Additional information

Supported by the NNSF of China (Grant Nos. 11761029, 11461049, 11371185, 11661034 and 11761055), the NSF of Inner Mongolia (Grant No. 2017MS0123), and the key Science and Technology Program of Colleges and Universities of Inner Mogolia (Grant No. NJZY17234)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, X.H., Huang, J.J. & Alatancang On the Origin and Numerical Range of Bounded Operators. Acta. Math. Sin.-English Ser. 35, 1715–1722 (2019). https://doi.org/10.1007/s10114-019-8478-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-019-8478-2

Keywords

MR(2010) Subject Classification

Search

Navigation