(untitled) (Baghdad Science Journal, 2010)
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.