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NEW BROWDER AND WEYL TYPE THEOREMS

  • Berkani, Mohammed (Department of mathematics Operator Theory Team Science Faculty of Oujda University Mohammed I) ;
  • Kachad, Mohammed (Department of mathematics Operator Theory Team Science Faculty of Oujda University Mohammed I)
  • Received : 2013.10.10
  • Published : 2015.03.31

Abstract

In this paper we introduce and study the new properties ($W_{\Pi}$), ($UW_{{\Pi}_a}$), ($UW_E$) and ($UW_{\Pi}$). The main goal of this paper is to study relationship between these new properties and other Weyl type theorems. Moreover, we reconsider several earlier results obtained respectively in [11], [18], [14], [1] and [13] for which we give stronger versions.

Keywords

References

  1. M. Amouch and M. Berkani, On the property (gw), Mediterr. J. Math. 3 (2008), no. 3, 371-378.
  2. M. Berkani, On a class of quasi-Fredholm operators, Integral Equations Operator Theory 34 (1999), no. 2, 244-249. https://doi.org/10.1007/BF01236475
  3. M. Berkani, Restriction of an operator to the range of its powers, Studia Math. 140 (2000), no. 2, 163-175.
  4. M. Berkani, Index of B-Fredholm operators and generalization of a Weyl theorem, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1717-1723. https://doi.org/10.1090/S0002-9939-01-06291-8
  5. M. Berkani, B-Weyl spectrum and poles of the resolvent, J. Math. Anal. Appl. 272 (2002), no. 2, 596-603. https://doi.org/10.1016/S0022-247X(02)00179-8
  6. M. Berkani, On the equivalence of Weyl theorem and generalized Weyl theorem, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 1, 103-110. https://doi.org/10.1007/s10114-005-0720-4
  7. M. Berkani and A. Arroud, Generalized Weyl's theorem and hyponormal operators, J. Aust. Math. Soc. 76 (2004), no. 2, 291-1302. https://doi.org/10.1017/S144678870000896X
  8. 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.
  9. M. Berkani and M. Kachad, New Weyl-type Theorems. I, Funct. Anal. Approx. Comput. 4 (2012), no. 2, 41-47.
  10. M. Berkani, M. Kachad, H. Zariouh, and H. Zguitti, Variations on a-Browder's Theorem, Sarajevo. J. Math. 9 (2013), no. 2, 271-281. https://doi.org/10.5644/SJM.09.2.11
  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. https://doi.org/10.1017/S0017089501030075
  13. M. Berkani and H. Zariouh, Extended Weyl type theorems, Math. Bohem. 134 (2009), no. 4, 369-378.
  14. S. V. Djordjevic and Y. M. Han, Browder's theorems and spectral continuity, Glasg. Math. J. 42 (2000), 479-486. https://doi.org/10.1017/S0017089500030147
  15. H. Heuser, Functional Analysis, John Wiley & Sons Inc, New York, 1982.
  16. S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), no. 2, 317-337. https://doi.org/10.2969/jmsj/03420317
  17. K. B. Laursen and M.M. Neumann, An introduction to Local Spectral Theory, Clarendon Press Oxford, 2000.
  18. V. Rakocevic, Operators obeying a-Weyl's theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), no. 10, 915-919.
  19. H. Weyl, Uber beschrankte quadratische Formen, deren Differenz vollstetig ist, Rend. Circ. Mat. Palermo 27 (1909), 373-392. https://doi.org/10.1007/BF03019655
  20. H. Zariouh and H. Zguitti, Variations on Browder's theorem, Acta Math. Univ. Comenian. 81 (2012), no. 2, 255-264.