Perturbation of spectra of operator matrices and local spectral theory

For A ∈ L(X), B ∈ L(Y ) and C ∈ L(Y,X) we denote by MC the operator defined on X ⊕ Y by A C 0 B . In this article, we study defect set DΣ = (Σ(A) ∪ Σ(B)) \ Σ(MC) for different spectra including the spectrum, the essential spectrum, Weyl spectrum and the approximate point spectrum. We then apply the obtained results to the stability of such spectra (DΣ =∅) and the classes of operators C for which stability holds of MC using local spectral theory. © 2005 Published by Elsevier Inc