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PERTURBATIONS OF SPECTRA OF OPERATOR MATRICES

DRAGAN S. DJORDJEVIĆ
Journal of Operator Theory
Vol. 48, No. 3, Supplement (2002), pp. 467-486
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24715580
Page Count: 20
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PERTURBATIONS OF SPECTRA OF OPERATOR MATRICES
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Abstract

In this article MC denotes a 2 × 2 operator matrix of the form ${\mathrm{M}}_{\mathrm{C}}=\left[\begin{array}{cc}\mathrm{A}& \mathrm{C}\\ 0& \mathrm{B}\end{array}\right]$, which is acting on the product of Banach or Hilbert spaces X ⊕ Y. We investigate sets $\underset{\mathrm{C}\in \mathcal{L}(\mathrm{Y},\mathrm{X})}{\bigcap }{\mathrm{\sigma }}_{\mathrm{\tau }}\left({\mathrm{M}}_{\mathrm{C}}\right)$, where στ(MC) can be equal to the left (right), essential, left (right) Fredholm, Weyl or Browder spectrum of MC. Thus, generalizations and extensions of various well-known and recent results of H. Du and J. Pan (Proc. Amer. Math. Soc. 121 (1994), 761–766), J.K. Han, H.Y. Lee and W.Y. Lee (Proc. Amer. Math. Soc. 128 (2000), 119–123) and W.Y. Lee (Proc. Amer. Math. Soc. 129 (2000), 131–138) are presented.

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