Browder essential approximate point spectra and hypercyclicity for operator matrices Original Research Article

When Aset membership, variantB(H) and Bset membership, variantB(K) are given, we denote by MC the operator acting on the infinite dimensional separable Hilbert space Hcircled plusK of the form image. 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 Cset membership, variantB(K,H). In addition, we explore the hypercyclicity and supercyclicity for 2 × 2 upper triangular operator matrices on the Hilbert space.