Local Spectral Theory and Surjective Spectrum of Linear Relations.

We initiate a study of local spectral theory for linear relations. At the beginning, we define the local spectrum and study its properties. Then we obtain results related to the correlation analytic core K′(T) and the quasinilpotent part H0(T) of a linear relation T in a Banach space X. As an application, we present a characterization of the surjective spectrum 𝜎su(T) in terms of the local spectrum and show that if X = H0(⋋I − T) + K′(⋋I − T), then 𝜎su(T) does not cluster at ⋋. [ABSTRACT FROM AUTHOR]