Abstract
We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Aiena, Fredholm and local spectral theory, with application to multipliers. Kluwer Acad. Publishers, 2004.
Aiena P.: Classes of Operators Satisfying a-Weyl’s theorem. Studia Math. 169, 105–122 (2005)
Aiena P.: Property (w) and perturbations II. J. Math. Anal. and Appl. 342, 830–837 (2008)
Aiena P.: Quasi Fredholm operators and localized SVEP. Acta Sci. Math. (Szeged) 73, 251–263 (2007)
Aiena P., Aponte E., Bazan E.: Weyl type theorems for left and right polaroid operators. Int. Equa. Oper. Theory 66, 1–20 (2010)
Aiena P., Biondi M.T.: Property (w) and perturbations. J. Math. Anal. and Appl. 336, 683–692 (2007)
Aiena P., Biondi M.T., Carpintero C.: On Drazin invertibility. Proc. Amer. Math. Soc. 136, 2839–2848 (2008)
Aiena P., Biondi M.T., Villafãne F.: Property (w) and perturbations III. J. Math. Anal. and Appl. 353, 205–214 (2009)
Aiena P., Carpintero C., Rosas E.: Some characterization of operators satisfying a-Browder theorem. J. Math. Anal. Appl. 311, 530–544 (2005)
Aiena P., Guillen J., Peña P.: Property (w) for perturbations of polaroid operators. Linear Algebra and its Appl. 428, 1791–1802 (2008)
Aiena P., Peña P.: A variation on Weyl’s theorem. J. Math. Anal. Appl. 324, 566–579 (2006)
Aiena P., Sanabria J.E.: On left and right Drazin invertibility. Acta Sci. Math. (Szeged), 74, 669–687 (2008)
Aiena P., Villafañe F.: Weyl’s theorem for some classes of operators. Int. Equa. Oper. Theory 53, 453–466 (2005)
An J., Han Y.M.: Weyl’s theorem for algebraically Quasi-class A operators. Int. Equa. Oper. Theory 62, 1–10 (2008)
Berkani M., Sarih M.: On semi B-Fredholm operators. Glasgow Math. J. 43, 457–465 (2001)
M. Berkani, H. Zariouh, New extended Weyl type theorems. (2009), preprint.
Coburn L.A.: Weyl’s theorem for nonnormal operators. Michigan Math. J. 20, 529–544 (1970)
Curto R.E., Han Y.M.: Weyl’s theorem, a-Weyl’s theorem, and local spectral theory. J. London Math. Soc. (2) 67, 499–509 (2003)
D. S. Djordjević, Operators obeying a-Weyl’s theorem. Publicationes Math. Debrecen 55, 3-4, no. 3 (1999), 283-298.
Duggal B.P.: Hereditarily polaroid operators, SVEP and Weyl’s theorem. J. Math. Anal. Appl. 340, 366–373 (2008)
Harte R., Woo Young Lee: Another note on Weyl’s theorem. Trans. Amer. Math. Soc. 349, 2115–2124 (1997)
Heuser H.: Functional Analysis. Marcel Dekker, New York (1982)
Kato T.: Perturbation theory for linear operators. Springer-Verlag, New York (1966)
Laursen K.B., Neumann M.M.: Introduction to local spectral theory. Clarendon Press, Oxford (2000)
Oudghiri M.: Weyl’s and Browder’s theorem for operators satysfying the SVEP. Studia Math. 163(1), 85–101 (2004)
Rako cević V.: On a class of operators. Mat. Vesnik 37, 423–426 (1985)
Rako cević V.: Operators obeying a-Weyl’s theorem. Rev. Roumaine Math. Pures Appl. 34(10), 915–919 (1989)
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by Fondi ex-60 2007, Universitá di Palermo. The other two authors were supported by CDCHT of Universidad de Los Andes, project NURR-C-511-09-05-B.
Rights and permissions
About this article
Cite this article
Aiena, P., Guillén, J.R. & Peña, P. Property (R) for Bounded Linear Operators. Mediterr. J. Math. 8, 491–508 (2011). https://doi.org/10.1007/s00009-011-0113-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-011-0113-0