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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aiena, P.: Fredholm and Local Spectral Theory II, with Application to Weyl-type Theorems. Springer Lecture Notes of Mathematics 2235, (2018)
Aiena, P.: Algebraically paranormal operators on Banach spaces. Banach J. Math. Anal. 7(2), 136–145 (2013)
Aiena, P., Aponte, E.: Polaroid type operators under perturbations. Studia Math. 214, 121–136 (2013)
Aiena, P., Aponte, E., Bazan, E.: Weyl type theorems for left and right polaroid operators. Integral Equ. Oper. Theory 66, 1–20 (2010)
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)
Aiena, P., Peña, P.: A variation on Weyl’s theorem. J. Math. Anal. Appl. 324, 566–79 (2006)
Aiena, P., Triolo, S.: Weyl type theorems on Banach spaces under compact perturbations. Mediterr. J. Math. 15, Issue 3, 1 June 2018, Article number 126
Coburn, L.A.: Weyl’s theorem for nonnormal operators. Mich. Math. J. 13(3), 285–288 (1966)
Conway, J.B.: The Theory of Subnormal Operators. Mathematical Survey and Monographs, vol. 36. American Mathematical Society, Providence; Springer, New York (1992)
Douglas, R.G.: Banach Algebra Techniques in Operator Theory. Graduate Texts in Mathematics, vol. 179, 2nd edn. Springer, New York (1998)
Duggal, B.P.: Hereditarily polaroid operators, SVEP and Weyl’s theorem. J. Math. Anal. Appl. 340, 366–73 (2008)
Duggal, B.P., Kim, I.H.: Generalized Browder, Weyl spectra and the polaroid property under compact perturbations. Mat. Vesnik 54(1), 281–302 (2017)
Farenick, D.R., Lee, W.Y.: Hyponormality and spectra of Toeplitz operators. Trans. Am. Math. Soc. 348(no. 10), 4153–74 (1996)
Heuser, H.: Functional Analysis. Marcel Dekker, New York (1982)
Laursen, K.B., Neumann, M.M.: Introduction to Local Spectral Theory. Clarendon Press, Oxford (2000)
Li, C.G., Zhou, T.T.: Polaroid type operators and compact perturbations. Studia Math. 221, 175–192 (2014)
Oudghiri, M.: Weyl’s and Browder’s theorem for operators satisfying the SVEP. Studia Math. 163(1), 85–101 (2004)
Putinar, M.: Hyponormal operators are subscalar. J. Oper. Theory 12, 385–95 (1984)
Widom, H.: On the spectrum of Toeplitz operators. Pac. J. Math. 14, 365–75 (1964)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aiena, P., Triolo, S. Some Remarks on the Spectral Properties of Toeplitz Operators. Mediterr. J. Math. 16, 135 (2019). https://doi.org/10.1007/s00009-019-1397-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-019-1397-8