Ascent and essential ascent spectrum of linear relations

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Ascent and essential ascent spectrum of linear relations

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Title: Ascent and essential ascent spectrum of linear relations
Author: Chafai, Ezzeddine; Mnif, Maher
Abstract: In the present paper, we study the ascent of a linear relation everywhere defined on a Banach space X and the related essential ascent spectrum. Some properties and characterization of such spectra are given. In particular, we show that a Banach space X is finite dimensional if and only if the ascent and the essential ascent of every closed linear relation in X is finite. As an application, we focus on the stability of the ascent and the essential ascent spectrum under perturbations. We prove that an operator F in X has some finite rank power, if and only if, σ_asc^e(T + F) = σ_asc^e (T), for every closed linear relation T commuting with F.
URI: http://hdl.handle.net/10662/8966
Date: 2016


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