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

 

A note on the spectrum of an upper triangular operator matrix


Authors: Mohamed Barraa and Mohamed Boumazgour
Journal: Proc. Amer. Math. Soc. 131 (2003), 3083-3088
MSC (1991): Primary 47A10, 47A55, 47B47
Published electronically: January 28, 2003
MathSciNet review: 1993217
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Abstract: Let $M_C= [\begin{smallmatrix} A& C \\ 0 & B \\ \end{smallmatrix}] $ be a $2\times 2$ upper triangular operator matrix acting on the Banach space $E\oplus F$. We investigate the set of the operators $C$ for which $\sigma(M_C)=\sigma(A)\cup\sigma(B)$, where $\sigma(.)$ denotes the spectrum.


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Additional Information

Mohamed Barraa
Affiliation: Département de Mathématiques, Faculté des Sciences Semlalia, B.P 2390, Marrakech, Maroc
Email: barraa@hotmail.com

Mohamed Boumazgour
Affiliation: Département de Mathématiques, Faculté des Sciences Semlalia, B.P 2390, Marrakech, Maroc
Address at time of publication: Département de Mathématiques et Statistique, Pavillon Alexandre Vachon, Université Laval, Québec, Canada G1K 7P4
Email: boumazgour@ucam.ac.ma, boumazgo@mat.ulaval.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06862-X
PII: S 0002-9939(03)06862-X
Keywords: Spectrum, $2\times 2$ upper triangular operator matrix, generalized derivation
Received by editor(s): March 1, 2002
Received by editor(s) in revised form: April 23, 2002
Published electronically: January 28, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society