Browder spectra for upper triangular operator matrices

When A ∈ B(H) and B ∈ B(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space H ⊕K of the form MC = A C 0 B . In this paper, we prove that C∈B(K,H) σb(MC) = σab(A) ∪ σab B ∗ ∪ λ ∈ C: n(A −λI ) +n(B −λI ) = d(A−λI ) +d(B −λI ) , where σb(T ), σab(T ), n(T ), d(T ) and T ∗ denote the Browder spectrum, Browder essential approximate point spectrum, nullity, deficiency and conjugate of T , respectively. Some related results are obtained. © 2007 Elsevier Inc. All rights reserved.