Browder essential approximate point spectra and hypercyclicity for 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 . In this paper, it is shown that if A is upper semi-Fredholm of finite ascent and infinite codimension, and if R(B) is closed of infinite kernel, then MC is upper semi-Fredholm of finite ascent for some C∈B(K,H). In addition, we explore the hypercyclicity and supercyclicity for 2 × 2 upper triangular operator matrices on the Hilbert space.