Skip to main content
Log in

Single-Valued Extension Property and Property \((\omega)\)

  • Research Articles
  • Published:
Functional Analysis and Its Applications Aims and scope

Abstract

We study the stability of the single-valued extension property for operators on a Hilbert space. Further, relations between the stability of the single-valued extension property and of property \((\omega)\) are given.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Aiena, Fredholm and Local Spectral Theory, Lecture Notes in Math., 2235 Springer-Verlag, 2019.

    MATH  Google Scholar 

  2. P. Aiena and O. Garcia, “Generalized Browder’s Theorem and SVEP”, Mediterr. J. Math., 4:2 (2007), 215–228.

    Article  MathSciNet  Google Scholar 

  3. P. Aiena and M. T. Biondi, “Property \((\omega)\) and perturbations”, J. Math. Anal. Appl., 336:1 (2007), 683–692.

    Article  MathSciNet  Google Scholar 

  4. P. Aiena and P. Peña, “Variations on Weyl’s theorem”, J. Math. Anal. Appl., 324:1 (2006), 566–579.

    Article  MathSciNet  Google Scholar 

  5. M. Berkani, M. Sarih, and H. Zariouh, “Browder-type theorems and SVEP”, Mediterr. J. Math., 8:3 (2011), 399–409.

    Article  MathSciNet  Google Scholar 

  6. I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, New York–London–Paris, 1968.

    MATH  Google Scholar 

  7. J. B. Conway, A Course in Functional Analysis, Grad. Text in Math., 96 Springer-Verlag, New York, 1990.

    MATH  Google Scholar 

  8. N. Dunford, “A survey of the spectral operators”, Bull. Amer. Math. Soc., 64 (1958), 217–274.

    Article  MathSciNet  Google Scholar 

  9. J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, The Clarendon Press, Oxford University Press, New York, 1996.

    MATH  Google Scholar 

  10. D. A. Herrero, Approximation of Hilbert Space Operators, vol. 1, Pitman Research Notes in Mathematics Series, 224 Longman Scientific and Technical, Hasrlow, 1989.

    Google Scholar 

  11. D. A. Herrero, T. J. Taylor, and Z. Y. Wang, “Variation of the point spectrum under compact perturbations”, Topics in Operator Theory, Oper. Theory Adv. Appl., 32 Birkäuser, Basel, 1988, 113–158.

    Article  MathSciNet  Google Scholar 

  12. C. L. Jiang and Z. Y. Wang, Structures of Hilbert Space Operators, World Scientific Publishing, Hackensack, 2006.

    Book  Google Scholar 

  13. K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Math. Soc. Monographs, New Ser., 20 The Clarendon Press, Oxford University Press, New York, 2000.

    MATH  Google Scholar 

  14. C. G. Li, S. Zhu, and Y. L. Feng, “Weyl’s theorem for functions of operators and approximation”, Inregral Equations Operator Theory, 67:4 (2010), 481–497.

    Article  MathSciNet  Google Scholar 

  15. V. Rakočević, “On a class of operators”, Mat. Vesnik, 37:4 (1985), 423–426.

    MathSciNet  MATH  Google Scholar 

  16. W. J. Shi and X. H. Cao, “Property \((\omega)\) and its perturbations”, Acta Math. Sinica, 30:5 (2014), 797–804.

    Article  MathSciNet  Google Scholar 

  17. A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley & Sons, New York–Chichester–Brisbane, 1980.

    MATH  Google Scholar 

  18. S. Zhu and C. G. Li, “SVEP and compact perturbations”, J. Math. Anal. Appl., 380:1 (2011), 69–75.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the reviewers and editors for their help, comments, and suggestions, which improved this paper.

Funding

This research was supported by the Fundamental Research Funds for the Central Universities (GK202007002).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lili Yang.

Additional information

Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2021, Vol. 55, pp. 78-90 https://doi.org/10.4213/faa3853.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, L., Cao, X. Single-Valued Extension Property and Property \((\omega)\). Funct Anal Its Appl 55, 316–325 (2021). https://doi.org/10.1134/S0016266321040067

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0016266321040067

Keywords

Navigation