G- Cyclicity And Somewhere Dense Orbit - Zeana Zaki Jamil (مجلة بغداد للعلوم)
let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of  with 1. An operator T is called G-cyclic over S if there is a non-zero vector xÎ H such that {aTn  x½aÎS, n ≥0} is norm-dense in H. Bourdon and Feldman have proved that the existence of somewhere dense orbits implies hypercyclicity. We show the corresponding result for G-cyclicity.