DOI QR코드

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SPECTRA ORIGINATED FROM FREDHOLM THEORY AND BROWDER'S THEOREM

  • Amouch, Mohamed (Department of Mathematics University Chouaib Doukkali Faculty of Sciences) ;
  • Karmouni, Mohammed (Multidisciplinary Faculty Cadi Ayyad University) ;
  • Tajmouati, Abdelaziz (Laboratory of Mathematical Analysis and Applications University Faculty of Sciences Dhar Al Mahraz)
  • 투고 : 2017.07.11
  • 심사 : 2017.12.29
  • 발행 : 2018.07.31

초록

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

키워드

참고문헌

  1. P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic Publishers, Dordrecht, 2004.
  2. P. Aiena, Semi-Fredholm Operator, Perturbation Theory and Localized SVEP, Merida. Venezuela, 2007.
  3. P. Aiena and M. T. Biondi, Ascent, descent, quasi-nilpotent part and analytic core of operators, Mat. Vesnik 54 (2002), no. 3-4, 57-70.
  4. P. Aiena, M. T. Biondi, and C. Carpintero, On Drazin invertibility, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2839-2848. https://doi.org/10.1090/S0002-9939-08-09138-7
  5. M. Amouch and M. Berkani, On the property (gw), Mediterr. J. Math. 5 (2008), no. 3, 371-378. https://doi.org/10.1007/s00009-008-0156-z
  6. M. Amouch and H. Zguitti, On the equivalence of Browder's and generalized Browder's theorem, Glasg. Math. J. 48 (2006), no. 1, 179-185. https://doi.org/10.1017/S0017089505002971
  7. M. Amouch and H. Zguitti, B-Fredholm and Drazin invertible operators through localized SVEP, Math. Bohem. 136 (2011), no. 1, 39-49.
  8. 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
  9. E. Boasso, Isolated spectral points and Koliha-Drazin invertible elements in quotient Banach algebras and homomorphism ranges, Math. Proc. R. Ir. Acad. 115A (2015), no. 2, 15 pp.
  10. W. Bouamama, Operateurs pseudo-Fredholm dans les espaces de Banach, Rend. Circ. Mat. Palermo (2) 53 (2004), no. 3, 313-324. https://doi.org/10.1007/BF02875724
  11. M. D. Cvetkovic and SC. Zivkovic-Zlatanovic, Generalized Kato decomposition and essential spectra, Complex Anal. Oper. Theory 11 (2017), no. 6, 1425-1449. https://doi.org/10.1007/s11785-016-0626-4
  12. Q. Jiang and H. Zhong, Generalized Kato decomposition, single-valued extension property and approximate point spectrum, J. Math. Anal. Appl. 356 (2009), no. 1, 322-327. https://doi.org/10.1016/j.jmaa.2009.03.017
  13. Q. Jiang and H. Zhong, Components of generalized Kato resolvent set and single-valued extension property, Front. Math. China 7 (2012), no. 4, 695-702. https://doi.org/10.1007/s11464-012-0207-4
  14. J. J. Koliha, Isolated spectral points, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3417-3424. https://doi.org/10.1090/S0002-9939-96-03449-1
  15. V. Kordula, V. Muller, and V. Rakocevic, On the semi-Browder spectrum, Studia Math. 123 (1997), no. 1, 1-13.
  16. J.-P. Labrousse, Les operateurs quasi Fredholm: une generalisation des operateurs semi Fredholm, Rend. Circ. Mat. Palermo (2) 29 (1980), no. 2, 161-258. https://doi.org/10.1007/BF02849344
  17. T. J. Laffey and T. T. West, Fredholm commutators, Proc. Roy. Irish Acad. Sect. A 82 (1982), no. 1, 129-140.
  18. M. Mbekhta, Generalisation de la decomposition de Kato aux operateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), no. 2, 159-175. https://doi.org/10.1017/S0017089500006807
  19. M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), no. 3, 621-631. https://doi.org/10.1090/S0002-9939-1990-1004421-1
  20. V. Muller and M. Mbekhta, On the axiomatic theory of spectrum. II, Studia Math. 119 (1996), no. 2, 129-147. https://doi.org/10.4064/sm-119-2-129-147
  21. M. O. Searcoid, Economical finite rank perturbations of semi-Fredholm operators, Math. Z. 198 (1988), no. 3, 431-434. https://doi.org/10.1007/BF01184676
  22. A. Tajmouati, M. Amouch, and M. Karmouni, Symmetric difference between pseudo B-Fredholm spectrum and spectra originated from Fredholm theory, Filomat 31(16) (2017), 5057-5064. https://doi.org/10.2298/FIL1716057T
  23. A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, second edition, John Wiley & Sons, New York, 1980.
  24. P. Vrbova, On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23(98) (1973), 483-492.
  25. H. Zariouh and H. Zguitti, On pseudo B-Weyl operators and generalized Drazin invertibility for operator matrices, Linear Multilinear Algebra 64 (2016), no. 7, 1245-1257. https://doi.org/10.1080/03081087.2015.1082959
  26. Q. Zeng, H. Zhong, and K. Yan, An extension of a result of Djordjevicand its applications, Linear Multilinear Algebra 64 (2016), no. 2, 247-257. https://doi.org/10.1080/03081087.2015.1034067