Spectra of operators with Bishop’s property $(\beta )$
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- by M. Drissi, M. El Hodaibi and E. H. Zerouali PDF
- Proc. Amer. Math. Soc. 136 (2008), 1609-1617 Request permission
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 $(\beta )$.References
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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
- 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
- © Copyright 2008 American Mathematical Society
- 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
- MathSciNet review: 2373590