G- Cyclicity And Somewhere Dense Orbit

Authors

Zeana Zaki Jamil

Abstract

let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of C with 1. An operator T is called G-cyclic over S if there is a non-zero vector xє H such that {αT^n x| αєS, 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.

Article Type

Article

How to Cite this Article

Jamil, Zeana Zaki (2010) "G- Cyclicity And Somewhere Dense Orbit," Baghdad Science Journal: Vol. 7: Iss. 2, Article 29.
DOI: https://doi.org/10.21123/bsj.2010.11927