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

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.