Essential point spectra of operator matrices trough local spectral theory

Abstract

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)) {set minus} 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.