College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710062, People's Republic of China ; Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
Abstract:
A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system acting on a separable Hilbert space into itself. It is proved that the wandering vector multipliers for a unitary group form a group, which gives a positive answer for a problem of Han and Larson. Furthermore, non-abelian unitary groups of order 6 are considered. We prove that the wandering vector multipliers of such a unitary group can not generate . This negatively answers another of their problems.