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GENERALIZED WEYL`S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS
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 Title & Authors
GENERALIZED WEYL`S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS
Zhou, Ting Ting; Li, Chun Guang; Zhu, Sen;
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 Abstract
Let be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on to satisfy that obeys generalized Weyl`s theorem for each function analytic on some neighborhood of . Also we investigate the stability of generalized Weyl`s theorem under (small) compact perturbations.
 Keywords
generalized Weyl`s theorem;operator approximation;compact perturbations;
 Language
English
 Cited by
 References
1.
P. Aiena, Property (w) and perturbations. II, J. Math. Anal. Appl. 342 (2008), no. 2, 830-837. crossref(new window)

2.
P. Aiena and M. Berkani, Generalized Weyl's theorem and quasiaffinity, Studia Math. 198 (2010), no. 2, 105-120. crossref(new window)

3.
P. Aiena and M. T. Biondi, Property (w) and perturbations, J. Math. Anal. Appl. 336 (2007), no. 1, 683-692. crossref(new window)

4.
P. Aiena, M. T. Biondi, and F. Villafane, Property (w) and perturbations. III, J. Math. Anal. Appl. 353 (2009), no. 1, 205-214. crossref(new window)

5.
M. Amouch, Weyl type theorems for operators satisfying the single-valued extension property, J. Math. Anal. Appl. 326 (2007), no. 2, 1476-1484. crossref(new window)

6.
I. J. An and Y. M. Han, Weyl's theorem for algebraically quasi-class A operators, Integral Equations Operator Theory 62 (2008), no. 1, 1-10. crossref(new window)

7.
S. K. Berberian, An extension of Weyl's theorem to a class of not necessarily normal operators, Michigan Math. J. 16 (1969), 273-279. crossref(new window)

8.
M. Berkani, Index of B-Fredholm operators and generalization of a Weyl theorem, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1717-1723 (electronic). crossref(new window)

9.
M. Berkani, On the equivalence of Weyl theorem and generalized Weyl theorem, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 1, 103-110. crossref(new window)

10.
M. Berkani and A. Arroud, Generalized Weyl's theorem and hyponormal operators, J. Aust. Math. Soc. 76 (2004), no. 2, 291-302. crossref(new window)

11.
M. Berkani and J. J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), no. 1-2, 359-376.

12.
M. Berkani and M. Sarih, On semi B-Fredholm operators, Glasg. Math. J. 43 (2001), no. 3, 457-465.

13.
X. H. Cao, Topological uniform descent and Weyl type theorem, Linear Algebra Appl. 420 (2007), no. 1, 175-182. crossref(new window)

14.
X. H. Cao, M. Z. Guo, and B. Meng, Weyl type theorems for p-hyponormal and M- hyponormal operators, Studia Math. 163 (2004), no. 2, 177-188. crossref(new window)

15.
L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285-288. crossref(new window)

16.
J. B. Conway, A course in Functional Analysis, second ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990.

17.
R. E. Curto and Y. M. Han, Generalized Browder's and Weyl's theorems for Banach space operators, J. Math. Anal. Appl. 336 (2007), no. 2, 1424-1442. crossref(new window)

18.
B. P. Duggal, Hereditarily polaroid operators, SVEP and Weyl's theorem, J. Math. Anal. Appl. 340 (2008), no. 1, 366-373. crossref(new window)

19.
N. Dunford and J. T. Schwartz, Linear Operators. Part I, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1988.

20.
D. A. Herrero, Economical compact perturbations. II. Filling in the holes, J. Operator Theory 19 (1988), no. 1, 25-42.

21.
D. A. Herrero, Approximation of Hilbert Space Operators. Vol. 1, second ed., Pitman Research Notes in Mathematics Series, vol. 224, Longman Scientific & Technical, Harlow, 1989.

22.
C. G. Li, S. Zhu, and Y. L. Feng, Weyl's theorem for functions of operators and ap- proximation, Integral Equations Operator Theory 67 (2010), no. 4, 481-497. crossref(new window)

23.
H. Radjavi and P. Rosenthal, Invariant Subspaces, second ed., Dover Publications Inc., Mineola, NY, 2003.

24.
H. Weyl, Uber beschrankte quadratische formen, deren differenz, vollsteig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392. crossref(new window)

25.
H. Zguitti, A note on generalized Weyl's theorem, J. Math. Anal. Appl. 316 (2006), no. 1, 373-381. crossref(new window)

26.
S. Zhu and C. G. Li, SVEP and compact perturbations, J. Math. Anal. Appl. 380 (2011), no. 1, 69-75. crossref(new window)