Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON WEIGHTED BROWDER SPECTRUM

  • Received : 2020.04.09
  • Accepted : 2021.10.29
  • Published : 2022.01.31
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Abstract

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

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References

  1. 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
  2. P. Aiena and S. Triolo, Weyl-type theorems on Banach spaces under compact perturbations, Mediterr. J. Math. 15 (2018), no. 3, Paper No. 126, 18 pp. https://doi.org/10.1007/s00009-018-1176-y
  3. S. C. Arora and P. Dharmarha, On weighted Weyl spectrum. II, Bull. Korean Math. Soc. 43 (2006), no. 4, 715-722. https://doi.org/10.4134/BKMS.2006.43.4.715
  4. N. Athmouni, H. Baloudi, A. Jeribi, and G. Kacem, On weighted and pseudo-weighted spectra of bounded operators, Commun. Korean Math. Soc. 33 (2018), no. 3, 809-821. https://doi.org/10.4134/CKMS.c170245
  5. 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
  6. C. R. Carpintero, O. Garc'ia, E. R. Rosas, and J. E. Sanabria, B-Browder spectra and localized SVEP, Rend. Circ. Mat. Palermo (2) 57 (2008), no. 2, 239-254. https://doi.org/10.1007/s12215-008-0017-4
  7. G. Edgar, J. Ernest, and S. G. Lee, Weighing operator spectra, Indiana Univ. Math. J. 21 (1971/72), 61-80. https://doi.org/10.1512/iumj.1971.21.21005
  8. M. A. Kaashoek and D. C. Lay, Ascent, descent, and commuting perturbations, Trans. Amer. Math. Soc. 169 (1972), 35-47. https://doi.org/10.2307/1996228