HYPERCYCLICITY AND WEYI, TYPE THEOREMS FOR OPERATOR MATRICES

Abstract

In this paper, we study the hypercyclicity and supercyclicity for operator matrices in the class S consisting 2 x 2 operator matrices with (1,2)-entries having closed range. Under some conditions, we find the necessary and sufficient conditions for 2 x 2 operator matrices in the class S for which Weyl's theorem, Browder's theorem, a-Weyl's theorem or a-Bmwder's theorem hold.