An operator T on a complex separable infinite dimensional Hilbert space is hypercyclic if there is a vector \(y \in \cal{H}\) such that the orbit Orb(T, y) = {y, Ty, T2y, T3y, …} is dense in \(\cal{H}\) . Hypercyclic property and supercyclic proeprty are liable to fail for 2 × 2 upper triangular operator matrices. In this paper, we aim to explore and characterize the hypercyclicity and the supercyclicity for 2 × 2 upper triangular operator matrices. We obtain a spectral characterization of the norm-closure of the class of all hypercyclic (supercyclic) operators for 2 × 2 upper triangular operator matrices.
