SpringerLink
Log in

\(({P},\;m)\)-B-normal and quasi-P-B-normal operators in semi-Hilbert spaces

  • Original Paper
  • Published:
Advances in Operator Theory Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new family of operators which is called polynomially-m-B-normal (resp-quasi polynomially B-normal). Some of the basic properties of members of these families are studied.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Al Mohammady, S., Beinane, Sid Ahmed O., M Sid Ahmed O. A.: On \((n,m)\)-\(A\)-normal and \((n,m)\)-\(A\)-quasinormal Semi-Hilbert space operators (preprint)

  2. Arias, M.L., Corach, G., Gonzalez, M.C.: Partial isometries in semi-Hilbertian spaces. Linear Algebra Appl. 428(7), 1460–1475 (2008)

    Article  MathSciNet  Google Scholar 

  3. Arias, M.L., Corach, G., Gonzalez, M.C.: Metric properties of projections in semi-Hilbertian spaces. Integral Equ. Oper. Theory 62(1), 11–28 (2008)

    Article  MathSciNet  Google Scholar 

  4. Arias, M.L., Corach, G., Gonzalez, M.C.: Lifting properties in operator range. Acta Sci. Math. (Szeged) 75(3–4), 635–653 (2009)

    MathSciNet  Google Scholar 

  5. Benali, A., Sid Ahmed M.O.A.: \((\alpha ,\beta ))\)-\(A\)-Normal Operators in Semi-Hilbertian Spaces. Afrika Matematika ISSN 1012-9405 (2019)

  6. Chō, M., Na, B.N.: \(\breve{c}\) tovska: Spectral properties of \(n\)-normal operators. Filomat 32(14), 5063–5069 (2018)

    Article  MathSciNet  Google Scholar 

  7. Chō, M., Lee, J.E., Tanahashic, K., Uchiyamad, A.: Remarks on \(n\)-normal operators. Filomat 32(15), 5441–5451 (2018)

    Article  MathSciNet  Google Scholar 

  8. Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, Berlin (1990)

    Google Scholar 

  9. Djordjević D. S., ChŌ, M., Mosić, D.: Pollynomialy normal operators. Ann. Funct. Anal. 11, 493–504 (2020)

  10. Douglas, R.G.: On majorization, factorization and range inclusion of operators on Hilbert space. Proc. Am. Math. Soc. 17, 413–415 (1966)

    Article  MathSciNet  Google Scholar 

  11. Jibril, A.S.: On \(n\)-power normal operators. J. Sci. Eng. 33(2A), 247–251 (2008)

    MathSciNet  Google Scholar 

  12. Hamidou, J.S.: Class of \((A, n)\)-power-quasi-hyponormal operators in semi-Hilbertian spaces. Int. J. Pure Appl. Math. 93(1), 61–83 (2014)

    Google Scholar 

  13. Moslehian, M.S., Kian, M., Xu, Q.: Positivity of \(2\times 2\) block matrices of operators. Banach J. Math. Anal. 13(3), 726–743 (2019)

    Article  MathSciNet  Google Scholar 

  14. Moslehian, M. S.: On \((\alpha , \beta )\)-Normal Operators in Hilbert Spaces. IMAGE 39, Problem 39-4 (2007)

  15. Saddi, A.: \(A\)-normal operators in semi-Hilbertian spaces. Aust. J. Math. Anal. Appl. 9(1), 1–12 (2012)

    MathSciNet  Google Scholar 

  16. Sid Ahmed, M.O.A., Ahmed, O.B.: On the classes \((n, m)\)- power \(D\)-normal and \((n, m)\)-power \(D\)-quasinormal operators. Oper. Matrices 13(3), 705–732 (2019)

    MathSciNet  Google Scholar 

  17. Sid Ahmed O. B., Polynomially \(A\)-normal operators in semi-Hilbertian spaces. Jouf Univ. Sci. Eng. J. 7(1), 18–25 (2020)

Download references

Acknowledgements

The author would like to thank the anonymous reviewers for their careful reading of the manuscript.

Author information

Authors and Affiliations

  1. Mathematical Analysis and Applications Mathematics Department, College of Science, Jouf University, P.O.Box 2014, Sakaka, Saudi Arabia

    Naeem Ahmad

Authors
  1. Naeem Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Naeem Ahmad.

Additional information

Communicated by S. Djordjevic.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, N. \(({P},\;m)\)-B-normal and quasi-P-B-normal operators in semi-Hilbert spaces. Adv. Oper. Theory 6, 19 (2021). https://doi.org/10.1007/s43036-020-00118-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s43036-020-00118-x

Keywords

Mathematics Subject Classification

Search

Navigation