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Generalisation de la decomposition de kato aux opérateurs paranormaux et spectraux

  • Mostafa Mbekhta (a1)

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Dans tout ce qui suit, H désigne un espace de Hilbert séparable, A un opérateur fermé de domaine D(A) dans H, on note B(H) l'ensemble des opérateurs bornés de H dans lui-même et N(A), R(A) respectivement le noyau de A, l'image de A.

En 1958, T. Kato a démontré dans [7] le théorème suivant.

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References

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1.Albrecht, E., A characterization of spectral operators on Hilbert spaces, Glasgow Math. J. 23 (1982), 9195.
2.Apostol, C., Quasi-affine transform of quasinilpotent compact operators, Rev. Roumaine Math. Pures Appl. 21 (1976), 813816.
3.Colojoara, I. et Foias, C., Theory of generalized spectral operators (Gordon and Breach, New York, 1968).
4.Dunford, N. et Schwartz, J., Linear operators, Part III: Spectral operators(Wiley Interscience, New York, 1971).
5.Kaashoek, K. H. Forster et M. A., The asymptotic behaviour of the reduced minimum modulus of a Fredholm operator, Proc. Amer. Math. Soc. 49, (1975), 123131.
6.Goldberg, S., Unbounded linear operators (McGraw-Hill, New York, 1966).
7.Kato, T., Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261322.
8.Labrousse, J. P., Les opérateurs quasi-Fredholm, Rend. Circ. Mat. Palermo (2) XXIX (1980), 161258
9.Mbekhta, M., Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux (Thèse 3ème cycle, Université de Nice, 1984)
10.Saphar, P., Contribution à l'étude des applications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363384
11.Taylor, A., Introduction to functional analysis (Wiley, 1958)
12.Nashed, M. Z., Perturbations and approximations for generalized inverses and linear operator equations, Generalized inverses and applications, (Ed. Nashed, Z., Academic Press, 1976), 325396
13.Vasilescu, F. H., Analytic functional calculus and spectral decompositions (Reidel, 1982).
14.Vrbova, P., On local spectral properties of operators in Banach spaces, Czechoslovak Math. J. 23 (1973), 483492.

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