Journal of University of Chinese Academy of Sciences >
Generalized property (ω') of finite rank perturbations of operators
Received date: 2010-10-08
Revised date: 2010-11-23
Online published: 2011-11-15
We define the generalized property (ω'), a variant of Weyl's theorem. By means of the new spectrum defined in view of the property of consistency in Fredholm and index, we consider the preservation of generalized property (ω') under a finite rank perturbation commuting with T, whenever T is a-isoloid. The theory is illustrated in the case of some special classes of operators.
LIU Jun-Ying , CAO Xiao-Hong . Generalized property (ω') of finite rank perturbations of operators[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(6) : 707 -714 . DOI: 10.7523/j.issn.2095-6134.2011.6.001
[1] Weyl H. Vber beschrnkte quadratische Formen, deren Differenz vollstetig ist
[J]. Rendiconti del Circolo Matematico di Palermo, 1909, 27: 373-392.
[2] Harte R, Lee W Y. Another note on Weyl's theorem
[J]. Transactions of the American Mathematical Society, 1997, 349: 2115-2124.
[3] Rakocevic V. On a class of operators
[J]. Matematicki Vesnik, 1985, 37: 423-426.
[4] Rakocevic V. Operators obeying a-Weyl's theorem
[J]. Revue Roumaine de Mathématique Pures, 1989, 34(10): 915-919.
[5] Cao X H, Liu J Y. Consistent Fredholm and index operators and generalized property(ω')
[J]. Acta Mathematica Sinica, 2010, 53(5): 953-962(in Chinese). 曹小红,刘俊英. 一致Fredholm指标算子及广义(ω')性质
[J]. 数学学报,2010,53(5):953-962.
[6] Berkani M. On a class of quasi-Fredholm operators
[J]. Integral Equations and Operator Theory, 1999, 34: 244-249.
[7] Berkani M. Index of B-Fredholm operators and generalization of a Weyl theorem
[J]. Proceedings of the American Mathematical Society, 2002, 130: 1717-1723.
[8] Cao X H. Weyl spectrum of the products of operators
[J]. Journal of the Korean Mathematical Society, 2008, 45(3): 771-780.
[9] Berkani M, Koliha J J. Weyl type theorems for bounded linear operators
[J]. Acta Mathematica Scientia, 2003, 69: 359-376.
[10] Oberai K K. On the Weyl spectrum II
[J]. Illinois Journal of Mathematics, 1997, 21: 84-90.
[11] Taylor A E. Theorems on ascent, descent, nullity and defect of linear operators
[J]. Mathematische Annalen, 1996, 163: 18-49.
[12] Cao X H, Guo M Z, Meng B. Weyl spectra and Weyl's theorem
[J]. Journal of Mathematical Analysis and Applications, 2003, 288: 758-767.
[13] Berkani M. B-Weyl spectrum and poles of the resolvent
[J]. Journal of Mathematical Analysis and Applications, 2002, 272: 596-603.
[14] Herrero D A. Limits of hypercyclic and supercyclic operators
[J]. Journal of Functional Analysis, 1991, 99: 179-190.
[15] Aiena P, Biondi M T. Property (ω) and perturbations
[J]. Journal of Mathematical Analysis and Applications, 2007, 336: 683-692.
/
| 〈 |
|
〉 |