A note on Weyl’s theorem for operator matrices

Djordjević, Slaviša; Han, Young Min

doi:10.1090/S0002-9939-02-06808-9

A note on Weyl’s theorem for operator matrices
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by Slaviša V. Djordjević and Young Min Han

Proc. Amer. Math. Soc. 131 (2003), 2543-2547

DOI: https://doi.org/10.1090/S0002-9939-02-06808-9

Published electronically: November 27, 2002

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