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Spectra of operators with Bishop's property $ (\beta)$


Authors: M. Drissi, M. El Hodaibi and E. H. Zerouali
Journal: Proc. Amer. Math. Soc. 136 (2008), 1609-1617
MSC (2000): Primary 47AXX, 47BXX
DOI: https://doi.org/10.1090/S0002-9939-08-08947-8
Published electronically: January 8, 2008
MathSciNet review: 2373590
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Abstract: Let $ X$ be a Banach space and let $ \mathcal{A}(X)$ be the class that consists of all operators $ T\in\mathcal{L}(X)$ such that for every $ \lambda\in\mathbb{C}$, the range of $ (T-\lambda I)$ has a finite-codimension when it is closed. For an integer $ n\in\mathbb{N}$, we define the class $ \mathcal{A}_{n}(X)$ as an extension of $ \mathcal{A}(X)$. We then study spectral properties of such operators, and we extend some known results of multi-cyclic operators with $ (\beta)$.


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Additional Information

M. Drissi
Affiliation: Département de Mathématiques, Université Mohammed premier, Oujda, Maroc
Email: m22drissi@yahoo.fr

M. El Hodaibi
Affiliation: Département de Mathématiques, Université Mohammed premier, Oujda, Maroc
Email: hodaibi2001@yahoo.fr

E. H. Zerouali
Affiliation: Département de Mathématiques et Informatique, Université Mohammed V, BP 1014 Rabat, Maroc
Email: zerouali@fsr.ac.ma

DOI: https://doi.org/10.1090/S0002-9939-08-08947-8
Keywords: Spectra, multi-cyclic operators, quasi-similar operators, Bishop's property $(\beta )$
Received by editor(s): April 23, 2006
Received by editor(s) in revised form: September 18, 2006
Published electronically: January 8, 2008
Additional Notes: The research of the first and second authors was supported in part by a project of the Université Mohamed premier, Faculté des sciences, Oujda, Maroc.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society

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