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

 

Weyl spectra of operator matrices


Author: Woo Young Lee
Journal: Proc. Amer. Math. Soc. 129 (2001), 131-138
MSC (1991): Primary 47A53, 47A55
Published electronically: July 27, 2000
MathSciNet review: 1784020
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Abstract:

In this paper it is shown that if $M_{C}=\left (\begin{smallmatrix}A&C\ 0&B\end{smallmatrix}\right )$ is a $2\times 2$ upper triangular operator matrix acting on the Hilbert space $\mathcal{H}\oplus \mathcal{K}$ and if $\omega (\cdot )$ denotes the ``Weyl spectrum", then the passage from $\omega (A)\cup \omega (B)$ to $\omega (M_{C})$ is accomplished by removing certain open subsets of $\omega (A) \cap \omega (B)$ from the former, that is, there is equality \begin{equation*}\omega (A)\cup \omega (B)=\omega (M_{C}) \cup \mathfrak{S}, \end{equation*} where $\mathfrak{S}$ is the union of certain of the holes in $\omega (M_{C})$ which happen to be subsets of $\omega (A)\cap \omega (B)$.


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Additional Information

Woo Young Lee
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Email: wylee@yurim.skku.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05846-9
PII: S 0002-9939(00)05846-9
Keywords: Weyl spectrum, Weyl's theorem, operator matrices
Received by editor(s): November 21, 1997
Received by editor(s) in revised form: May 1, 1998, and March 10, 1999
Published electronically: July 27, 2000
Additional Notes: This work was supported by the BSRI(96-1420) and KOSEF through the GARC at Seoul National University.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society