Skip to main content
SpringerLink
Log in

Selfadjoint operators and symmetric operators

  • Published:
Acta Scientiarum Mathematicarum Aims and scope Submit manuscript

Abstract

Our study is in the set {ie529-1}(H) of all semiclosed operators in a Hilbert space H. We show that the set {ie529-2}(H) of all selfadjoint operators is relatively open in the set {ie529-3}(H) of all semiclosed symmetric operators. We calculate the value of a radius of minus-Laplacian -Δ. As a topological approach, we show the selfadjointness of the Schrodinger operator with a Kato.Rellich potential.

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. T. Ando, De Branges Spaces and Analytic Operator Functions, Lecture note, Hokkaido University, Sapporo, Japan, 1990.

    MATH  Google Scholar 

  2. R. G. Douglas, On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc., 17 (1966), 413–416.

    MATH  Google Scholar 

  3. G. Hirasawa, A topology for semiclosed operators in a Hilbert space, Acta Sci. Math. (Szeged), 73 (2007), 271–282.

    MathSciNet  MATH  Google Scholar 

  4. G. Hirasawa, A metric for unbounded linear operators in a Hilbert space, Integr. Equ. Oper. Theory, 70 (2011), 363–378.

    Article  MathSciNet  Google Scholar 

  5. S. Izumino, Quotients of bounded operators, Proc. Amer. Math. Soc., 106 (1989), 427–435.

    Article  MathSciNet  Google Scholar 

  6. T. Kato, Perturbation Theory for Linear Operators, Reprint of the 1980 Edition, Springer.

  7. W. E. Kaufman, Representing a closed operator as a quotient of continuous operators, Proc. Amer. Math. Soc., 72 (1978), 531–534.

    Article  MathSciNet  Google Scholar 

  8. W. E. Kaufman, Semiclosed operators in Hilbert space, Proc. Amer. Math. Soc., 76 (1979), 67–73.

    Article  MathSciNet  Google Scholar 

  9. K. Schmüdgen, Unbounded Selfadjoint Operators on Hilbert Space, Springer.

  10. Z. Sebestyén and Zs. Tarcsay, Characterizations of selfadjoint operators, Studia Sci. Math. Hungar., 50 (2013), 423–435.

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author would like to thank the referee for his/her careful reading of the manuscript and useful comments about the proof of Theorem 1.1.

Author information

Authors and Affiliations

  1. College of Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Japan

    Go Hirasawa

Authors
  1. Go Hirasawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Go Hirasawa.

Additional information

Communicated by L. Kérchy

This work was supported by the Grant-in-Aid for Scientific Research (C), No. 24540160, from the Japan Society for the Promotion of Science.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hirasawa, G. Selfadjoint operators and symmetric operators. ActaSci.Math. 82, 529–543 (2016). https://doi.org/10.14232/actasm-015-044-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.14232/actasm-015-044-4

Key words and phrases

AMS Subject Classification

Search

Navigation