Journal of Operator Theory

Volume 48, Issue 3, Supplementary 2002 pp. 467-486.

Perturbations of spectra of operator matrices

Authors: Dragan S. Djordjevic
Author institution: University of Nis, Faculty of Sciences and Mathematics, Department of Mathematics, Cirila i Metodija 2, 18000 Nis, Yugoslavia

Summary: In this article $M_C$ denotes a $2\times 2$ operator matrix of the form $M_C=\left[\matrix{ A&C\cr0&B}\right]$, which is acting on the product of Banach or Hilbert spaces $X\oplus Y$. We investigate sets $\bigcap\limits_{C\in \L(Y,X)}\sigma_\tau(M_C)$, where $\sigma_\tau(M_C)$ can be equal to the left (right), essential, left (right) Fredholm, Weyl or Browder spectrum of $M_C$. Thus, generalizations and extensions of various well-known and recent results of H. Du and J. Pan ({\it Proc. Amer. Math. Soc.} {\bf 121} (1994), 761--766), J.K. Han, H.Y. Lee and W.Y. Lee ({\it Proc. Amer. Math. Soc.} {\bf 128} (2000), 119--123) and W.Y. Lee ({\it Proc. Amer. Math. Soc.} {\bf 12} 9 (2000), 131--138) are presented.

Keywords: Left and right spectra, essential spectrum, left and right Fredholm spectra, Weyl and Browder spectra, perturbations of spectra

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