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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectra of upper triangular operator matrices


Authors: C. Benhida, E. H. Zerouali and H. Zguitti
Journal: Proc. Amer. Math. Soc. 133 (2005), 3013-3020
MSC (2000): Primary 47A11, 47A10
Published electronically: March 24, 2005
MathSciNet review: 2159780
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07812-3
PII: S 0002-9939(05)07812-3
Keywords: Local spectral theory, operator matrices, spectra
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
Article copyright: © Copyright 2005 American Mathematical Society