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

## Main Article Content

### 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.

## Article Details

### References

- F. Abdmouleh, A. Ammar and A. Jeribi, Stability of the S-essential spectra on a Banach space. Math. Slovaca 63(2) (2013), 299-320.
- 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.
- 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.
- 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.
- T. Alvarez, R.W. Cross and D. Wilcox, Multivalued Fredholm Type Operators With Abstract Generalised Inverses, J. Math. Anal. Appl. 261 (2001), 403-417.
- A. Ammar, A characterization of some subsets of essential spectra of a multivalued linear operator, Complex Anal. Oper. Theory 11(1) (2017), 175-196.
- A. Ammar, S. Fakhfakh and A. Jeribi, Relatively bounded perturbation and essential approximate point and defect spectrum of linear relations, prepint (2017).
- 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.
- R.W. Cross, Multivalued Linear Operators, Marcel Dekker Inc. (1998).
- A. Jeribi, Spectral Theory and Applications of Linear Operators and Block Operator Matrices, Springer-Verlag. New York (2015).
- 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.