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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 Weyl's theorem for operator matrices


Authors: Slavisa V. Djordjevic and Young Min Han
Journal: Proc. Amer. Math. Soc. 131 (2003), 2543-2547
MSC (2000): Primary 47A10, 47A55
Published electronically: November 27, 2002
MathSciNet review: 1974653
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Abstract: When $A\in\mathcal B(X)$ and $B\in\mathcal B(Y)$ are given we denote by $M_C$ an operator acting on the Banach space $X\oplus Y$of the form

\begin{displaymath}M_{C}=\left (\begin{matrix}A&C\\ 0&B\end{matrix}\right), \ \text{where} \ C\in \mathcal B(Y,X). \end{displaymath}

In this note we examine the relation of Weyl's theorem for $A\oplus B$ and $M_C$ through local spectral theory.


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Additional Information

Slavisa V. Djordjevic
Affiliation: University of Niš, Faculty of Science, P.O. Box 91, 18000 Niš, Yugoslavia
Email: slavdj@pmf.pmf.ni.ac.yu

Young Min Han
Affiliation: Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419
Email: yhan@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06808-9
PII: S 0002-9939(02)06808-9
Keywords: Upper triangular operator matrix, Weyl's theorem, single valued extension property
Received by editor(s): January 21, 2002
Received by editor(s) in revised form: March 27, 2002
Published electronically: November 27, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society