Two results are proved which concern Riesz points of upper triangular operator matrices. Applications are made to questions involving when Weyl's Theorem holds for an upper triangular operator matrix.

Abstract. The spectra of the 2 × 2 upper triangular operator matrix M C = ( A C 0 B ) acting on a Hilbert space 𝐻₁ ⨁ 𝐻₂ are investigated. We obtain a necessary and sufficient condition of 𝜎 (𝑀𝐶) ...