Please use this identifier to cite or link to this item:
http://hdl.handle.net/10662/8966
Title: | Ascent and essential ascent spectrum of linear relations |
Authors: | Chafai, Ezzeddine Mnif, Maher |
Keywords: | Ascent;Essential ascent;Perturbation;Spectrum;Linear relations;Ascenso;Ascenso esencial;Perturbación;Espectro;Relaciones lineales |
Issue Date: | 2016 |
Publisher: | Universidad de Extremadura |
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 |
Appears in Collections: | Extracta Mathematicae Vol. 31, nº 2 (2016) |
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2605-5686_31_2_145.pdf | 152,03 kB | Adobe PDF | View/Open |
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