Abstract. We give a sufficient condition involving local spectra for an operator on a separable Banach space to be hypercyclic. Similar conditions are given for supercyclicity. These spectral conditions allow us to characterize the hyponormal operators with hypercyclic adjoints and those with supercyclic adjoints.

AMS Subject Classification (1991): 47A10, 47A11, 47A16, 47B20, 47B40

Keyword(s): Hypercyclic, supercyclic, hyponormal, (\beta ), (\delta ), propertiesand

Received February 7, 2001, and in final form October 2, 2001. (Registered under 2844/2009.)