Essential point spectra of operator matrices trough local spectral theory

For A ∈ B(X), B ∈ B(Y ) and C ∈ B(Y,X), let MC be the operator defined on X ⊕ Y by A C 0 B . In this paper, we study defect set (Σ(A) ∪ Σ(B)) \ Σ(MC), where Σ is the Browder spectrum, the essential approximate point spectrum and Browder essential approximate point spectrum. We then give application for Weyl’s and Browder’s theorems. © 2007 Elsevier Inc. All rights reserved