Ascent spectrum and essential ascent spectrum

• Autorzy: O. Bel Hadj Fredj , M. Burgos , M. Oudghiri
• Języki publikacji: EN

Abstrakty

EN

We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{asc}^{e}(T + F) = σ_{asc}^{e}(T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued extension property are also analyzed for operators with finite essential ascent.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47A55: Perturbation theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 1
• Strony: 59-73

Daty

wydano

2008

Twórcy

autor

O. Bel Hadj Fredj

• UFR de Mathématiques, UMR-CNRS 8524, Université de Lille 1, 59655 Villeneuve d'Ascq, France

autor

M. Burgos

• Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain

autor

M. Oudghiri

• Faculté des Sciences, Université d'Oujda, Oujda, Maroc

Identyfikatory

DOI

10.4064/sm187-1-3