Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators

Mebarki, Leila; Benharrat, Mohammed; Messirdi, Bekkai

Research Article

Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators

Leila Mebarki
Mohammed Benharrat
Bekkai Messirdi

Abstract

This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-A-K)^{-1}K or K(lambda-A-K)^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.

How to Cite

L. Mebarki, M. Benharrat, B. Messirdi, Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators, Int. J. Anal. Appl. 9 (2015), 83–89.

BibTeX

@article{Mebarki2015,
  author  = {Mebarki, Leila and Benharrat, Mohammed and Messirdi, Bekkai},
  title   = {Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators},
  journal = {Int. J. Anal. Appl.},
  volume  = {9},
  year    = {2015},
  pages   = {83--89},
  doi     = {}
}

References

[1] A. Brunel and D. Revuz, Quelques applications probabilistes de la quasi-compacit ´e. Ann. Inst. Henri et Poincar ´e, B 10(3) (1974), 301-337.
[2] H. Hennion and L. Herv ´e, Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness. Springer-Verlag Berlin Heidelberg (2001).
[3] K. Latrach, Essential spectra on spaces with the Dunford-Pettis property, J. Math. Anal. Appl., 233, (1999), 607-622.
[4] K. Latrach, A. Dehici, Fredholm, Semi-Fredholm Perturbations and Essential spectra, J. Math. Anal. Appl., 259 (2001), 277-301.
[5] K. Latrach, A. Dehici, Relatively strictly singular perturbations, Essential spectra, and Application to transport operators, J. Math. Anal. Appl., 252(2001), 767-789.
[6] K. Latrach, A. Jeribi, Some results on Fredholm operators, essential spectra, and application, J. Math. Anal. Appl., 225, (1998), 461-485.
[7] K. Latrach, J. Martin Paoli, Relatively compact-like perturbations, essensial spectra and application, J. Aust. Math. Soc. 77 (2004), 73-89.
[8] M. Mokhtar-Kharroubi, Time asymptotic behaviour and compactness in neutron transport theory, Euro. J. Mech., B Fluids, 11(1992), 39-68.
[9] M. Schechter, Invariance of essential spectrum, Bull. Amer. Math. Soc. 71 (1965), 365-367.
[10] K. Yosida, Quasi-completely continuous linear functional operations, Jap. Journ. of Math., 15 (1939), 297- 301.
[11] K. Yosida, Functional Analysis, Springer-Verlag Berlin Heiderlberg, 1980.
[12] K. Yosida, S. Kakutani, Operator-theoretical treatment of Markov's process and mean ergodic theorem, Ann. of Math., 42, (1941), 188-228.