| Abstrakt: |
Our objective in this paper is to show that, similarly to the case of normal operators, a normal linear relation on a Hilbert space H satisfies several notions related to the local spectral theory such as the single valued extension property (SVEP), Bishop and Dunford properties, and more generally the spectral decomposability. To that end, we shall start by introducing all those notions for a closed linear relation T on a Banach space X. Then, we will use an approach allowing us to establish that, as soon as a local spectral property holds for the orthogonal operator part of T, it will automatically hold for T. Finally, we will apply that approach on a normal linear relation to reach our objective. [ABSTRACT FROM AUTHOR] |
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