JOURNAL BROWSE
Search
Advanced SearchSearch Tips
WEYL TYPE-THEOREMS FOR DIRECT SUMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
WEYL TYPE-THEOREMS FOR DIRECT SUMS
Berkani, Mohammed; Zariouh, Hassan;
  PDF(new window)
 Abstract
The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum , where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property () and if , , then possesses property () if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)
 Keywords
property (gb);property (b);property (gw);direct sums;essential semi-B-Fredholm spectrum;
 Language
English
 Cited by
 References
1.
P. Aiena and P. Pena, A variation on Weyl's theorem, J. Math. Anal. Appl. 324 (2006), no. 1, 566-579. crossref(new window)

2.
M. Amouch and M. Berkani, On the property (gw), Mediterr. J. Math. 5 (2008), no. 3, 371-378. crossref(new window)

3.
M. Berkani, On a class of quasi-Fredholm operators, Integr. Equ. Oper. Theory 34 (1999), no. 2, 244-249. crossref(new window)

4.
M. Berkani, Index of B-Fredholm operators and generalization of a-Weyl's theorem, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1717-1723. crossref(new window)

5.
M. Berkani, N. Castro, and S. V. Djordjevic, Single valued extension property and generalized Weyl's theorem, Math. Bohem. 131 (2006), no. 1, 29-38.

6.
M. Berkani and J. J. Koliha, Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged) 69 (2003), no. 1-2, 359-376.

7.
M. Berkani and M. Sarih, On semi B-Fredholm operators, Glasg. Math. J. 43 (2001), no. 3, 457-465.

8.
M. Berkani and H. Zariouh, Extended Weyl type theorems, Math. Bohem. 134 (2009), no. 4, 369-378.

9.
S. Clary, Equality of spectra of quasisimilar hyponormal operators, Proc. Amer. Math. Soc. 53 (1975), no. 1, 88-90. crossref(new window)

10.
L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285-288. crossref(new window)

11.
S. V. Djordjevic and Y. M. Han, A note on Weyl's theorem for operator matrices, Proc. Amer. Math. Soc. 131 (2003), no. 8, 2543-2547. crossref(new window)

12.
B. P. Duggal and C. S. Kubrusly, Weyl's theorem for direct sums, Studia Sci. Math. Hungar. 44 (2007), no. 2, 275-290.

13.
A. Gupta and N. Kashyap, Generalized a-Weyl's theorem for direct sums, Mat. Vesnik 62 (2010), no. 4, 265-270.

14.
Y. M. Han and S. V. Djordjevic, a-Weyl's theorem for operator matrices, Proc. Amer. Math. Soc. 130 (2002), no. 3, 715-722. crossref(new window)

15.
R. E. Harte and W. Y. Lee, Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), no. 5, 2115-2124. crossref(new window)

16.
H. Heuser, Functional Analysis, John Wiley & Sons Inc, New York, 1982.

17.
K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, Clarendon, Oxford, 2000.

18.
D. C. Lay, Spectral analysis using ascent, descent, nullity and defect, Math. Ann. 184 (1970), 197-214. crossref(new window)

19.
W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131-138. crossref(new window)

20.
V. Rakocevic, On a class of operators, Mat. Vesnik 37 (1985), no. 4, 423-426.

21.
V. Rakocevic, Operators obeying a-Weyl's theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), no. 10, 915-919.

22.
S. Roch and B. Silbermann, Continuity of generalized inverses in Banach algebras, Studia Math. 136 (1999), no. 3, 197-227.