On Hypercyclicity and Local Spectrum

Let X be a complex Banach space, and L(X) be the space of bounded operators on X. Given T 2 L(X) and x 2 X denote by T (x) the local Spectrum of T at x. And the operator T is called hypercyclic, if orb(T; x) = X. In this paper, we will introduce a relationship between the local spectrum and hypercyclicity.