G-cyclist and somewhere dense orbit

الملخص EN

Let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semi group of with 1.

An operator T is called G-cyclic over S if there is a non-zero vector x € H such that {αTN xα S, 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-cyclist.