Essential approximate point spectra and Weyl's theorem for operator matrices

We also give the necessary and sufficient conditions for which MC is Weyl or MC is lower semi-Fredholm with nonnegative index for some C∈B(K,H). In addition, we explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem, and a-Browder's theorem survive for 2×2 upper triangular operator matrices on the Hilbert space.