Weyl's theorem for 2*2 upper triangular operator matrices

Abstract

Let H and K be complex infinite dimensional separable Hilbert spaces. We denote by M_C a 2*2 upper triangular operator matrix acting on H+K. In this paper, we mainly characterize the equivalent conditions for the 2*2 upper triangular operator matrices such that they satisfy Weyl's theorem using the features of the elements on the diagonal.