UDC 517.98 This paper initiates 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… Click to show full abstract
UDC 517.98 This paper initiates 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 $K\prime (T)$ and quasinilpotent part $H_0(T)$ of a linear relation $T$ in a Banach space $X$. As an application, we give a characterization of the surjective spectrum $\sigma_{su}(T)$ in terms of the local spectrum and show that if $X = H_0(\lambda I - T) + K\prime (\lambda I - T)$, then $\sigma_{su}(T)$ does not cluster at $\lambda$.
               
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