Advertisement

Some Remarks on the Spectral Properties of Toeplitz Operators

  • Pietro AienaEmail author
  • Salvatore Triolo
Article
  • 31 Downloads

Abstract

In this paper, we study some local spectral properties of Toeplitz operators \(T_\phi \) defined on Hardy spaces, as the localized single-valued extension property and the property of being hereditarily polaroid.

Keywords

Toeplitz operators localized single-valued extension property Weyl-type theorems 

Mathematics Subject Classification

Primary 47A10 47A11 Secondary 47A53 47A55 

Notes

References

  1. 1.
    Aiena, P.: Fredholm and Local Spectral Theory II, with Application to Weyl-type Theorems. Springer Lecture Notes of Mathematics 2235, (2018)Google Scholar
  2. 2.
    Aiena, P.: Algebraically paranormal operators on Banach spaces. Banach J. Math. Anal. 7(2), 136–145 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aiena, P., Aponte, E.: Polaroid type operators under perturbations. Studia Math. 214, 121–136 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Aiena, P., Aponte, E., Bazan, E.: Weyl type theorems for left and right polaroid operators. Integral Equ. Oper. Theory 66, 1–20 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Aiena, P., Neumann, M.M.: On the stability of the localized single-valued extension property under commuting perturbations. Proc. Am. Math. Soc. 141(6), 2039–50 (2013)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Aiena, P., Peña, P.: A variation on Weyl’s theorem. J. Math. Anal. Appl. 324, 566–79 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Aiena, P., Triolo, S.: Weyl type theorems on Banach spaces under compact perturbations. Mediterr. J. Math. 15, Issue 3, 1 June 2018, Article number 126Google Scholar
  8. 8.
    Coburn, L.A.: Weyl’s theorem for nonnormal operators. Mich. Math. J. 13(3), 285–288 (1966)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Conway, J.B.: The Theory of Subnormal Operators. Mathematical Survey and Monographs, vol. 36. American Mathematical Society, Providence; Springer, New York (1992)Google Scholar
  10. 10.
    Douglas, R.G.: Banach Algebra Techniques in Operator Theory. Graduate Texts in Mathematics, vol. 179, 2nd edn. Springer, New York (1998)CrossRefGoogle Scholar
  11. 11.
    Duggal, B.P.: Hereditarily polaroid operators, SVEP and Weyl’s theorem. J. Math. Anal. Appl. 340, 366–73 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Duggal, B.P., Kim, I.H.: Generalized Browder, Weyl spectra and the polaroid property under compact perturbations. Mat. Vesnik 54(1), 281–302 (2017)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Farenick, D.R., Lee, W.Y.: Hyponormality and spectra of Toeplitz operators. Trans. Am. Math. Soc. 348(no. 10), 4153–74 (1996)Google Scholar
  14. 14.
    Heuser, H.: Functional Analysis. Marcel Dekker, New York (1982)zbMATHGoogle Scholar
  15. 15.
    Laursen, K.B., Neumann, M.M.: Introduction to Local Spectral Theory. Clarendon Press, Oxford (2000)zbMATHGoogle Scholar
  16. 16.
    Li, C.G., Zhou, T.T.: Polaroid type operators and compact perturbations. Studia Math. 221, 175–192 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Oudghiri, M.: Weyl’s and Browder’s theorem for operators satisfying the SVEP. Studia Math. 163(1), 85–101 (2004)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Putinar, M.: Hyponormal operators are subscalar. J. Oper. Theory 12, 385–95 (1984)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Widom, H.: On the spectrum of Toeplitz operators. Pac. J. Math. 14, 365–75 (1964)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di IngegneriaUniversità di PalermoPalermoItaly

Personalised recommendations