The Local spectral theory and surjective spectrum of linear relations

Keywords: Linear relations, local spectrum, surjective spectrum, correlation analytic core, local and glocal spectral subspaces

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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Published
22.02.2021
How to Cite
Mnif, M., and A.-A. Ouled-Hmed. “The Local Spectral Theory and Surjective Spectrum of Linear Relations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 2, Feb. 2021, pp. 222 -37, doi:10.37863/umzh.v73i2.81.
Section
Research articles