Necessary conditions for extended spectral decomposable multivalued linear operators

Authors: YOSRA BARKAOUI, MAHER MNIF

Abstract: In this paper, we use subsets of the Riemann sphere and specific types of invariant linear subspaces to introduce the extended spectral decomposable multivalued linear operators (linear relations) in Banach spaces. We also introduce the extended Bishop's property, the extended relatively single-valued extension property and the extended Dunford's property. More importantly, we show that these properties are three necessary conditions for a linear relation to be extended spectral decomposable.

Keywords: Multivalued linear operators, extended spectrum, extended spectral decomposable multivalued linear operator, extended Bishop's property, extended Dunford's property

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