Journal of Operator Theory

Volume 56, Issue 2, Fall 2006 pp. 259-271.

The descent spectrum and perturbations

Authors: M. Burgos (1), A. Kaidi (2), M. Mbekhta (3) and M. Oudghiri (4)
Author institution: (1) Departamento de Algebra y Analisis Matematico, Universidad de Almeria, Almeria, 04120, Spain
(2) Departamento de Algebra y Analisis Matematico, Universidad de Almeria, Almeria, 04120, Spain
(3) UFR de Mathematiques, UMR-CNRS 8524, Universite Lille 1, Villeneuve d'Ascq, 59655, France
(4) UFR de Mathematiques, UMR-CNRS 8524, Universite Lille 1, Villeneuve d'Ascq, 59655, France

Summary: In the present paper we continue to study the descent spectrum of an operator on a Banach space. We obtain that a Banach space $X$ is finite-dimensional if and only if there exists a bounded operator $T$ on $X$ such that its commutant is formed by algebraic operators. We provide also an affirmative answer to a question of M.A. Kaashoek and D.C. Lay.

Keywords: Spectrum, descent, perturbation, semi-Fredholm.

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