Proceedings of the American Mathematical Society

Author(s): C. Benhida; E. H. Zerouali; H. Zguitti
Journal: Proc. Amer. Math. Soc. 133 (2005), 3013-3020.
MSC (2000): Primary 47A11, 47A10
Posted: March 24, 2005
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Abstract: Let

be given Banach spaces. For $A\in{\mathcal L}(X),\,B\in{\mathcal L}(Y)$ and $C\in{\mathcal L}(Y,X)$ , let

be the operator defined on $X\oplus Y$ by $M_C = [\begin{smallmatrix} A & C 0 & B \end{smallmatrix}]$ . We give sufficient conditions on

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.

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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

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