The Local spectral theory and surjective spectrum of linear relations
DOI:
https://doi.org/10.37863/umzh.v73i2.81Keywords:
Linear relations, local spectrum, surjective spectrum, correlation analytic core, local and glocal spectral subspacesAbstract
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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