Spectra of upper triangular operator matrices
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- by C. Benhida, E. H. Zerouali and H. Zguitti PDF
- Proc. Amer. Math. Soc. 133 (2005), 3013-3020 Request permission
Abstract:
Let $X, Y$ be given Banach spaces. For $A\in {\mathcal L}(X), B\in {\mathcal L}(Y)$ and $C\in {\mathcal L}(Y,X)$, let $M_C$ be the operator defined on $X\oplus Y$ by $M_C = [\begin {smallmatrix} A & C 0 & B \end {smallmatrix}]$. We give sufficient conditions on $C$ to get $\Sigma (M_C) = \Sigma (M_0),$ where $\Sigma$ runs over a large class of spectra. We also discuss the case of some spectra for which the latter equality fails.References
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Additional Information
- C. Benhida
- Affiliation: UFR de Mathématiques - CNRS-UMR 8524, Université de Lille 1, Bât M2, 59655 Villeuneuve cedex, France
- Email: benhida@math.univ-lille1.fr
- E. H. Zerouali
- Affiliation: Département de Mathématiques et Informatique, Faculté des Sciences de Rabat, BP 1014 Agdal, Rabat, Maroc
- Email: zerouali@fsr.ac.ma
- H. Zguitti
- Affiliation: Département de Mathématiques et Informatique, Faculté des Sciences de Rabat, BP 1014 Agdal, Rabat, Maroc
- Email: zguitti@hotmail.com
- Received by editor(s): February 26, 2004
- Received by editor(s) in revised form: May 18, 2004
- Published electronically: March 24, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3013-3020
- MSC (2000): Primary 47A11, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-05-07812-3
- MathSciNet review: 2159780