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G- Cyclicity And Somewhere Dense Orbit | ||
| Baghdad Science Journal | ||
| Article 1, Volume 7, Issue 2, 2010, Pages 1053-1055 | ||
| Author | ||
| Zeana Zaki Jamil | ||
| Abstract | ||
| 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 x H such that {Tn xS, 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. | ||
| Keywords | ||
| Hypercyclic operators; hypercyclic vectors; semigroup; somewhere dense set; everywhere dense set | ||
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