On Stabilized Point Spectra of Multivalued Systems

Abstract.

Let H be an infinite dimensional Hilbert space. Denote by Λ (E, F) the set of all $\lambda \in \mathbb{R}$ for which the multivalued system 0 ∈ (F − λ E) (x) admits a nonzero solution x ∈ H. One says that Λ (E, F) is the point spectrum of the pair (E, F). It is well known that Λ (E, F) does not behave in a stable manner with respect to perturbations in the argument (E, F). The purpose of this note is to study the outer-semicontinuous hull (or graph-closure) of the mapping Λ.