A New Stability of the S-Essential Spectrum of Multivalued Linear Operators

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Aymen Ammar, Slim Fakhfakh, Aref Jeribi

Abstract

We unfold in this paper two main results. In the first, we give the necessary assumptions for three linear relations $A$, $B$ and $S$ such that $\sigma_{eap,S}(A+B)= \sigma _{eap,S}(A)$ and $\sigma_{e\delta,S}(A+B)= \sigma_{e\delta,S}(A)$ is true. In the second, considering the fact that the linear relations $A$, $B$ and $S$ are not precompact or relatively precompact, we can show that $\sigma_{eap,S}(A+B)= \sigma_{eap,S}(A)$ is true.

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References

  1. F. Abdmouleh, A. Ammar and A. Jeribi, Stability of the S-essential spectra on a Banach space. Math. Slovaca 63(2) (2013), 299-320.
  2. F. Abdmouleh, T. Alvarez, A. Ammar and A.Jeribi, Spectral Mapping Theorem for Rakocevic and Schmoeger Essential Spectra of a Multivalued Linear Operator, Mediterr. J. Math, 12(3) (2015), 10191031.
  3. F. Abdmouleh and A. Jeribi, Gustafson, Weidman, Kato, Wolf, Schechter, Browder, Rakocevic and Schmoeger essential spectra of the sum of two bounded operators and application to a transport operator, Math. Nachr. 284(2-3) (2011), 166-176.
  4. T. Alvarez, A. Ammar and A.Jeribi, A characterization of some subsets of S-essential spectra of a multivalued linear operator, Colloq. Math. 135 (2014), 171186.
  5. T. Alvarez, R.W. Cross and D. Wilcox, Multivalued Fredholm Type Operators With Abstract Generalised Inverses, J. Math. Anal. Appl. 261 (2001), 403-417.
  6. A. Ammar, A characterization of some subsets of essential spectra of a multivalued linear operator, Complex Anal. Oper. Theory 11(1) (2017), 175-196.
  7. A. Ammar, S. Fakhfakh and A. Jeribi, Relatively bounded perturbation and essential approximate point and defect spectrum of linear relations, prepint (2017).
  8. A. Ammar, S. Fakhfakh and A. Jeribi, Stability of the essential spectrum of the diagonally and off-diagonally dominant block matrix linear relations, J. Pseudo-Differ. Oper. Appl. 7(4) (2016), 493-509.
  9. R.W. Cross, Multivalued Linear Operators, Marcel Dekker Inc. (1998).
  10. A. Jeribi, Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer-Verlag. New York (2015).
  11. A. Jeribi, N. Moalla and S. Yengui, S-essential spectra and application to an example of transport operators, Math. Methods Appl. Sci. 37(16) (2014), 2341-2353.