Spectra of upper triangular operator matrices

Benhida, C.; Zerouali, E.; Zguitti, H.

doi:10.1090/S0002-9939-05-07812-3

Spectra of upper triangular operator matrices
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by C. Benhida, E. H. Zerouali and H. Zguitti PDF

Proc. Amer. Math. Soc. 133 (2005), 3013-3020 Request permission

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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