Weyl’s theorem for 2 × 2 upper triangular operator matrices

Let H and K be complex infinite dimensional separable Hilbert spaces. We denote by M_C = {pmatrix} A & C \\ 0 & B {pmatrix} a 2 ×2 upper triangular operator matrix acting on H ⊕ K, where A ∈ B(H), B ∈ B(K) and C ∈ B(K,H). In this paper, we mainly characterize the equivalent conditions for the 2 × 2 upper triangular operator matrices such that they satisfyWeyl’s theorem using the features of the elements on the diagonal.