On the axiomatic theory of spectrum II

M. Mbekhta; V. Müller

Studia Mathematica (1996)

  • Volume: 119, Issue: 2, page 129-147
  • ISSN: 0039-3223

Abstract

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We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.

How to cite

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Mbekhta, M., and Müller, V.. "On the axiomatic theory of spectrum II." Studia Mathematica 119.2 (1996): 129-147. <http://eudml.org/doc/216290>.

@article{Mbekhta1996,
abstract = {We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.},
author = {Mbekhta, M., Müller, V.},
journal = {Studia Mathematica},
keywords = {spectral mapping theorem; ascent; descent; semiregular operators; quasi-Fredholm operators; kernels; ranges; spectral mapping property},
language = {eng},
number = {2},
pages = {129-147},
title = {On the axiomatic theory of spectrum II},
url = {http://eudml.org/doc/216290},
volume = {119},
year = {1996},
}

TY - JOUR
AU - Mbekhta, M.
AU - Müller, V.
TI - On the axiomatic theory of spectrum II
JO - Studia Mathematica
PY - 1996
VL - 119
IS - 2
SP - 129
EP - 147
AB - We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.
LA - eng
KW - spectral mapping theorem; ascent; descent; semiregular operators; quasi-Fredholm operators; kernels; ranges; spectral mapping property
UR - http://eudml.org/doc/216290
ER -

References

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  8. [8] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971),17-32. Zbl0203.45601
  9. [9] R. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89-107. Zbl0206.13301
  10. [10] M. A. Kaashoek, Stability theorems for closed linear operators, Indag. Math. 27 (1965), 452-466. Zbl0138.07601
  11. [11] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261-322. Zbl0090.09003
  12. [12] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. Zbl0148.12601
  13. [13] V. Kordula, The essential Apostol spectrum and finite-dimensional perturbations, to appear. Zbl0880.47005
  14. [14] V. Kordula and V. Müller, The distance from the Apostol spectrum, Proc. Amer. Math, Soc., to appear. Zbl0861.47008
  15. [15] V. Kordula and V. Müller, On the axiomatic theory of spectrum, this issue, 109-128. Zbl0857.47001
  16. [16] J. P. Labrousse, Les opérateurs quasi-Fredholm : une généralisation des opérateurs semi-Fredholm, y Rend. Circ. Mat. Palermo 29 (1980), 161-258. Zbl0474.47008
  17. [17] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105. Zbl0694.47002
  18. [18] M. Mbekhta et A. Ouahab, Opérateur semi-régulier dans un espace de Banach et théorie spectrale, Acta Sci. Math. (Szeged), to appear. Zbl0742.47001
  19. [19] M. Mbekhta et A. Ouahab, Contribution à la théorie spectrale généralisée dans les espaces de Banach, C. R. Acad. Sci. Paris 313 (1991), 833-836. Zbl0742.47001
  20. [20] V. Müller, On the regular spectrum, J. Operator Theory 31 (1994), 363-380. Zbl0845.47005
  21. [21] V. Rakočevič, Generalized spectrum and commuting compact perturbations, Proc. Edinburgh Math. Soc. 36 (1993), 197-208. Zbl0794.47003
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Citations in EuDML Documents

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  1. J. Koliha, M. Mbekhta, V. Müller, Pak Poon, Corrigendum and addendum: "On the axiomatic theory of spectrum II"
  2. M. Berkani, Dagmar Medková, A note on the index of B -Fredholm operators
  3. M. Amouch, H. Zguitti, B-Fredholm and Drazin invertible operators through localized SVEP
  4. Vladimír Müller, Axiomatic theory of spectrum III: semiregularities
  5. M. Berkani, Restriction of an operator to the range of its powers
  6. Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz, The index for Fredholm elements in a Banach algebra via a trace II
  7. M. Berkani, N. Castro, S. V. Djordjević, Single valued extension property and generalized Weyl’s theorem
  8. M. Amouch, H. Zguitti, A note on the a -Browder’s and a -Weyl’s theorems
  9. Vladimír Kordula, Vladimír Müller, Vladimir Rakočević, On the semi-Browder spectrum
  10. L. Lindeboom, H. Raubenheimer, On regularities and Fredholm theory

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